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The RD Sharma class 12 solution of Algebra of vectors exercise FBQ is one of the highly recommended solutions for the Class 12 CBSE students, it is preferred over NCERT when it comes for the preparation of maths. The RD Sharma class 12th exercise FBQ comes under consideration when a student faces difficulty in solving any question of the Algebra of vectors. The Class 12 RD Sharma chapter 22 exercise FBQ solution gives a brief explanation of each and every concept that has been mentioned in the book.

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Algebra of Vectors exercise Fill in the blanks question 1

Answer:-Hint:- To solve this equation, we solve this by

Answer:- If represent the side of a triangle taken in order that

Solution:-

Algebra of Vectors exercise Fill in the blanks question 2

Answer:-Hint:- To solve this equation ,we use right angle triangle formula.

Given:- In a parallelogram

Solution:- In

According to right triangle

According to right triangle

Algebra of Vectors exercise Fill in the blanks question 3

Answer:-Hint:- We use the section formula for finding coordinates of centroid.

Given:- If are the position vectors of the vectors of a triangle having its centroid at the origin then

Solution: Here the coordinates of

Here, given that centroid is at the origin

Therefore,

Algebra of Vectors exercise Fill in the blanks question 4

Answer:-Hint:- To solve this equation we will make triangle, then we will find modulus.

Given:-If are the positive vectors of vertices of an equilateral triangle having its circumcentre at the origin, then

Solution:-

Centroid of triangle

For an equilateral triangle the circumcentre coincide with the centroid. Therefore,

Algebra of Vectors exercise Fill in the blanks question 5

Answer:- 9Hint:- To solve this question we use where is constant.

Given:- If the vector are collinear then

Using

Then,

Therefore,

Algebra of Vectors exercise Fill in the blanks question 6

Answer:-Hint:-To solve this equation we use

Given:-Vector of magnitude units in the direction of the vector

Solution:- we have Vector of magnitude units in the direction of the vector

Algebra of Vectors exercise Fill in the blanks question 7

Answer:-Hint:- To solve this equation we take

Given:- If is the mid point of side of and , Then

Solution:- Let are the position vectors of respectively.

Algebra of Vectors exercise Fill in the blanks question 8

Answer:-Hint:- To solve this question we use,

Given:- The cosines of the angles made by the vector with the coordinates axes are

Solution:- Let makes with and axis respectively

Algebra of Vectors exercise Fill in the blanks question 9

Answer:-Hint:-To solve this equation, we use standard formula .

Given:-A vector of magnitude 6; making angle with x-axis; with y axis and an acute angle with z axis

Solution:-we have

We know that

Algebra of Vectors exercise Fill in the blanks question 10

Answer:-Hint:-To solve this equation, we use substitute method

Given:- If the vector are then ____

Solution:-

Comparing we get

From eq (ii) we make y the subject to the equation

Substitute for in the equation(i)

Solving eq(iii) & (iv)

Put the values of x in eq(iii)

Put the values of z in eq(ii)

Algebra of Vectors exercise Fill in the blanks question 11

Answer:-Hint:-To solve this equation, we use magnitude length.

Given:- If and are the position vector of A and B respectively, then the position vector of a point and produced such that

Solution:-here

We have

Then

External dimension

Algebra of Vectors exercise Fill in the blanks question 12

Answer:-Hint:-To solve this equation, we use reverse process of vectors

Given:-In a rectangular hexagon

Solution:-

we have …(i)

From figure we can see

Using (ii) , (iii) and (iv) in (i), we get

Algebra of Vectors exercise Fill in the blanks question 13

Answer:Hint:-To solve this equation, we split forms

Given:-If are five points ____

Solution:

Algebra of Vectors exercise Fill in the blanks question 14

Answer:-Hint:-To solve this equation we do method

Given:- are five coplanar, such that

Solution:-

Algebra of Vectors exercise Fill in the blanks question 15

Answer:-Hint:-To solve this we know that two lines are collinear

Given:-The vector and are non collinear if are collinear then x……

Solution:- Let

For collinear

Hence

Algebra of Vectors exercise Fill in the blanks question 16

Answer:-Hint:- To solve this we use triangle law of vector addition

Given:-If are five point in a plane such that then K IS….

Solution:-

[∴Triangle Law of Vector Addition]

Algebra of Vectors exercise Fill in the blanks question 17

Hint:-To solve this question we have to connect or add vectors

Given:-Let P be the point of intersection of the diagonal of a parallelogram and is any point If

Solution:-

Algebra of Vectors exercise Fill in the blanks question 19

Answer:-Hint:-To solve this equation we use mid-point formula

Given:-If are mid points of the side respectively of then

Solution:-

In are mid pts.

Let be the position vector of

Using mid point formula.

As is a mid point of

Similarly E and F are the mid points of AC and AB respectively

Now,

Algebra of Vectors exercise Fill in the blanks question 20

Answer:-Hint:- To solve this equation we use mid-point formula

Given:-The algebraic sum of the vector directed from the vectors to the mid points of the opposite side is equal to

Solution:-

Algebra of Vectors exercise Fill in the blanks question 21

Answer:-Hint:-To solve this question, we use magnitude formula.

Given:-The value of k for which is parallel to holds true are ---

Solution:-

Algebra of Vectors exercise Fill in the blanks question 22

Answer:-Hint:-To solve this equation we use rhombus in parallelogram.

Given:-The vector bisects the angle between the non-collinear and if ---

Solution:-Non-collinear vector & have found parallelogram

Algebra of Vectors exercise Fill in the blanks question 23

Answer:-Hint:-To solve this equation we use standard formula.

Given:-The position vectors of two points and are respectively. The position vectors of a point which divides the line segment joining and in the ratio is ----

Solution:-

Section formula:

Internal

The RD Sharma class 12 solution chapter 22 exercise FBQ is the fill-in-the-blank type question that covers the essential concepts of this chapter. The RD Sharma class 12th exercise FBQ consists of a total of 23 questions giving knowledge about the concepts mentioned below-

Scalar and Vector product

Addition and subtraction of vectors

Multiplication and division by a scalar quantity

Collinear and non-collinear

Unit vectors and position vector

Coplanar points

Here is a list of reasons why students should opt for the RD Sharma solutions chapter 22 exercise FBQ book:-

The RD Sharma class 12th exercise FBQ consists of exercises and questions that are prepared by professionals in the field of mathematics, and also give you help advice on how to solve questions easily without taking much time.

Students will find that using RD Sharma class 12 chapter 22 exercise FBQ solutions will help them solve homework questions as it has been found that teachers are likely to use these solutions for assigning homework tasks to students and also prepare question papers for terminal exams.

Students can also use the RD Sharma class 12th exercise FBQ for the preparation for JEE mains as these solutions are considered above NCERT so therefore it can help you rank in good numbers.

The syllabus of the RD Sharma class 12th exercise FBQ is regularly updated as in every year to match up to the level of NCERT and also so that no students lags in any chapter.

The RD Sharma class 12th exercise FBQ can be downloaded for free from the Career360 website.

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Download E-book- 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

1. What are the norms of the vector?

The length of the vector is referred to as the vector or the vector's magnitude. The length of a vector is a non-negative number that describes the extent of the vector in space, and is sometimes referred to as the vectors of magnitude or the norm

2. What are the directions of a vector?

The direction of a vector is the orientation of the vector, that is, the angle it makes with the x-axis.

3. What is the sum of vectors called?

The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the parallelogram method or the triangle method.

4. How much price do I have to pay to buy the RD Sharma solutions?

The RD Sharma solutions can be bought free of cost when you download it from the Careers360 website.

5. Does the RD Sharma solutions match up to the recent syllabus?

Yes, the RD Sharma books are revised every year to correspond to the syllabus of NCERT.

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