# RD Sharma Class 12 Exercise 24.1 Vector or Cross Product Solutions Maths-Download PDF Online

RD Sharma’s maths books are well known for their quality and authenticity. Still, many students find it challenging to solve the problems and lag. This problem is that a student is unable to find sources from where they can understand and learn the concepts. RD Sharma Class 12th Exercise 24.1 solutions have arrived to solve this issue with complete reliability on them.

The chapter ‘Vector or Cross Product’ solutions are available for access at ease for students. RD Sharma Class 12th Chapter 24 Exercise 24.1 is as per the latest CBSE guidelines to help students score exceptionally in their board examinations. RD Sharma Solutions Cross Products, Unit vectors, area of parallelogram determined by the vectors, area of triangles by vectors and verify laws by vectors are discussed in this chapter. The cross-product of two vectors being the third vector perpendicular to the two original vectors is the concept discussed here. 48 questions are given in this exercise. Class 12th RD Sharma Chapter 24 Exercise 24.1 Solutions are available in PDF format and downloaded for free.

## RD Sharma Class 12 Solutions Chapter 24 Vector or Cross Product - Other Exercise

- Chapter 24 -Vector or Cross Product -Ex-FBQ
- Chapter 24 -Vector or Cross Product -Ex-MCQ
- Chapter 24 -Vector or Cross Product- Ex-VSA

## Vector or Cross Product Excercise: 24.1

Vector or Cross Product exercise 24.1 question 1

Answer :Hint : To solve this equation by using determinate formula

Given :

find

Solution :

Vector or Cross Product exercise 24.1 question 2 (i)

Answer :Hint : To solve this equation we use determinate formula then magnitude formula

Given :

Find value

Solution :

Vector or Cross Product exercise 24.1 question 2 (ii)

Answer :Hint : To solve this equation we use determinate formula then magnitude formula

Given :

Solution :

Vector or Cross Product exercise 24.1 question 3 (i)

Answer :Hint : To solve this equation , use magnitude and

Given :

Solution :

Vector or Cross Product exercise 24.1 question 3 (ii)

Answer :Hint : To solve this equation we use

Given :

Solution :

Vector or Cross Product exercise 24.1 question 4

Answer :Hint : To solve this equation we suppose both terms in x and y then we use magnitude formula

Given :

Solution :

Vector or Cross Product exercise 24.1 question 5

Answer :Hint : To solve this we multiply by 2 as given then magnitude formula.

Given :

Find

Solution :

We need to find unit vector of b ()

Vector or Cross Product exercise 24.1 question 6

Answer :Hint : To solve this equation we put value in

Given :

Find

Solution :

...............(1)

...............(2)

Vector or Cross Product exercise 24.1 question 7 (i)

Answer :Hint : To solve this equation we solve

Given : magnitude=49

Solution :

Vector or Cross Product exercise 24.1 question 7 (ii)

Answer :Hint : To solve this equation we use unit vector formula

Given : magnitude = 3

Solution :

Vector or Cross exercise 24.1 question 8 (i)

Answer : 6 square unitsHint : To solve this we use area of parallelogram

Given :

Solution : Area of parallelogram

Vector or Cross Product exercise 24.1 question 8 (ii)

Answer :Hint : To solve this , we use area of parallelogram.

Given :

Solution : Area of parallelogram

Area of parallelogram

Vector or Cross Product exercise 24.1 question 8 (iii)

Answer :Hint : To solve this equation we use area of parallelogram

Given :

Solution : Area of parallelogram

Vector or Cross Product exercise 24.1 question 8 (iv)

Answer :Hint : To solve this equation we use area of parallelogram

Given

Solution :

Area of parallelogram

Area of parallelogram

Vector or Cross Product exercise 24.1 question 9 (i)

Answer :Hint : To solve this we use area of parallelogram formula

Given : Area of parallelogram

Solution :

Vector or Cross Product exercise 24.1 question 9 (ii)

Answer :Hint : To solve this we use area of parallelogram formula

Given :

Solution : Area of parallelogram

Vector or Cross Product exercise 24.1 question 9 (iii)

Answer :Hint : To solve this we use area of parallelogram formula

Given :

Solution :Area of parallelogram

Vector or Cross Product exercise 24.1 question 9 (iv)

Answer :Hint : To solve this we use area of parallelogram formula

Given :

Solution : Area of parallelogram

Vector or Cross Product exercise 24.1 question 10

Answer : not equalHint : To solve this w use determinant method

Given :

Solution :

Vector or Cross Product exercise 24.1 question 11

Answer : 6

Hint : To solve this we use formulaGiven :

Solution :

Vector or Cross Product exercise 24.1 question 12

Answer : These are unit vectors as well as perpendicularHint : To solve this , we do magnitude of one by one

Given :

Solution :

Vector or Cross Product exercise 24.1 question 13

Answer : 25Hint : To solve this formula

Given :

Solution :

Vector or Cross Product exercise 24.1 question 14

Answer :Hint : To solve this equation we use aband

Given :

Solution :

Vector or Cross Product exercise 24.1 question 15

Answer :Hint : Here m is the constant team

Given :

Solution :

Vector or Cross Product exercise 24.1 question 16

Answer :Hint : To solve this we use formula

Given :

Solution :

Vector or Cross Product exercise 24.1 question 17

Answer :Hint : To solution we know are parallel

Given :

Solution : 1) and are parallel

Or

- & are perpendicular

Vector or Cross Product exercise 24.1 question 18

Answer:

Hint : To solve this equation we useGiven :

Solution :

Similarly can be prove for others

this means perpendicular

this means perpendicular

This are together form orthonormal trial

Vector or Cross Product exercise 24.1 question 19

Answer :Hint : To solve this equation , we use determination method

Given :

Solution :

If is perpendicular to

is perpendicular to , perpendicular to

Vector or Cross Product exercise 24.1 question 20

Answer:To have

Hint:

To solve this we use formula

Given:

Solution :

Divide by abc

.......(i)

.......(ii)

.......(iii)

From (i),(ii) and (iii)

Vector or Cross Product exercise 24.1 question 21

Answer:Hint:

To solve this we use determinant method

Given:

Solution:

Vector or Cross Product exercise 24.1 question 22

Answer: Square unitsHint: use concept.

Given:

Solution:

Square units

Vector or Cross Product exercise 24.1 question 23

Answer:L.H.S = R.H.S

Hint:

To solve this we use formula

Given:

Solution:

Vector or Cross Product exercise 24.1 question 24

Answer:Hint:

Given:

Solution:

.........(1)

Also,

............(2)

Dividing equation (1) and (2)

Vector or Cross Product exercise 24.1 question 25

Answer: 7Hint:

To solve this we use formula

Given:

Solution:

Vector or Cross Product exercise 24.1 question 26

Answer:square units

Hint:

To solve this we use area of triangle formula

Given:

Solution:

square units

Vector or Cross Product exercise 24.1 question 27 (i)

Answer:Hint: To solve this we use determinant method

Given:

Solution:

D is perpendicular to a and b both. Hence, parallel to a*b

Vector or Cross Product exercise 24.1 question 27 (ii)

Answer:Hint:

To solve this question we suppose term in terms of x,y,z.

Given:

Solution: Let

Now,

.......(i)

Now,

....(ii)

Now,

....(iii)

Solving (2) and (3)

Putting value in (i)

Vector or Cross Product exercise 24.1 question 28

Answer:Hint:

To solve this we use determinant method

Given:

Solution:

Let

And

Let be any vector perpendicular to both , hence parallel to

Vector or Cross Product exercise 24.1 question 29

Answer:Hint:

To solve this we use area of triangle ABC

Given:

Solution:

Vector or Cross Product exercise 24.1 question 30

Answer:square units

Hint:

To solve this we use area of triangle

Given:

Solution:

Vector or Cross Product exercise 24.1 question 32

Answer:No, take any two collinear vectors

Hint:

To solve this we let

Given:

Solution:

Statement:

If either

Converse:

Let

But

Vector or Cross Product exercise 24.1 question 33

Answer:Proved

Hint:

To solve this we use determinant method

Given:

Solution:

Vector or Cross Product exercise 24.1 question 34

Answer:Square units

Hint:

To solve this we use area of triangle

Given:

Solution:

Vector or Cross Product exercise 24.1 question 35

Answer:Square units

Hint:

To solve this we use area of triangle

Given:

Solution:

Vector or Cross Product exercise 24.1 question 36

Hint:

To solve this we use determinant method

Given:

Solution:

Similarly

Area of the parallelogram

Vector or Cross Product exercise 24.1 question 37

Answer:4

Hint: To solve this we use formula

Given:

Solution:

Vector or Cross Product exercise 24.1 question 38

Answer:Hint: To solve this we use formula

Given:

Solution:

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## RD Sharma Chapter-wise Solutions

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

## Frequently Asked Question (FAQs) - RD Sharma Class 12 Exercise 24.1 Vector or Cross Product Solutions Maths-Download PDF Online

**Question: **How can I get an understanding of the key concepts in the RD Sharma Class 12th Exercise 24.1?

**Answer: **

Before the start of an academic year, every student should download and read the CBSE syllabus to get a good understanding of the concepts that will be covered in the exams.

**Question: **Will the RD Sharma Solutions for Class 12 help to score brilliant marks in the board exams?

**Answer: **

Yes, the RD Sharma Solutions for Class 12 is one of the best study materials which are available online. Chapter-wise and Exercise-wise solutions can be referred to by the students when they are not able to find or understand an accurate answer for the textbook questions.

**Question: **How can I avail the benefit from these solutions?

**Answer: **

You can visit the website, download the PDF for free and practice regularly to score good marks and avail full benefits.

**Question: **What do you mean by a cross product?

**Answer: **

A Cross product is a binary operation on two vectors in three-dimensional space.

**Question: **What is the formula cross product?

**Answer: **

If two vectors A and B have an angle θ, then the formula for the cross product of vectors is given by:

A × B = |A| |B| sin θ