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NCERT Solutions for Exercise 10.4 Class 12 Maths Chapter 10 Vector Algebra are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 10.4 Class 12 Maths chapter 10 discuss the questions related to cross product of vectors and their applications. Exercise 10.4 Class 12 Maths have 12 questions. All these 12 questions of NCERT solutions for Class 12 Maths chapter 10 exercise 10.4 are explained with all necessary steps. The Class 12 Maths chapter 10 exercise 10.4 solutions are designed by a mathematics expert and are in accordance with Class 12 CBSE patterns. Concepts of cross products are also explained in Class 11 NCERT Physics TextBooks in the chapter system of particles and rotational motion and are used in other chapters of Class 11 and 12 too. One question may be expected from the Class 12 Maths chapter 10 exercise 10.4 for Class 12 CBSE Class 12 Board Exam.
12th class Maths exercise 10.4 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Question:1 Find
Answer:
Given in the question,
and we need to find
Now,
So the value of is
Question:2 Find a unit vector perpendicular to each of the vector , where
Answer:
Given in the question
Now , A vector which perpendicular to both is
And a unit vector in this direction :
Hence Unit vector perpendicular to each of the vector is
.
Answer:
Given in the question,
angle between and
:
angle between and
angle with and
:
Now, As we know,
Now components of are:
Question:4 Show that
Answer:
To show that
LHS=
As product of a vector with itself is always Zero,
As cross product of a and b is equal to negative of cross product of b and a.
= RHS
LHS is equal to RHS, Hence Proved.
Question:5 Find and
if
Answer:
Given in the question
and we need to find values of and
From Here we get,
From here, the value of and
is
Question:6 Given that and . What can you conclude about the vectors
?
Answer:
Given in the question
and
When , either
are perpendicular to each other
When either
are parallel to each other
Since two vectors can never be both parallel and perpendicular at same time,we conclude that
Question:7 Let the vectors be given as
Then show that
Answer:
Given in the question
We need to show that
Now,
Now
Hence they are equal.
Question:8 If either then
. Is the converse true? Justify your answer with an example.
Answer:
No, the converse of the statement is not true, as there can be two non zero vectors, the cross product of whose are zero. they are colinear vectors.
Consider an example
Here
Hence converse of the given statement is not true.
Question:9 Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
Answer:
Given in the question
vertices A=(1, 1, 2), B=(2, 3, 5) and C=(1, 5, 5). and we need to find the area of the triangle
Now as we know
Area of triangle
The area of the triangle is square units
Question:10 Find the area of the parallelogram whose adjacent sides are determined by the vectors and
.
Answer:
Given in the question
Area of parallelogram with adjescent side and
,
The area of the parallelogram whose adjacent sides are determined by the vectors and
is
Question:11 Let the vectors be such that
, then
is a unit vector, if the angle between is
Answer:
Given in the question,
As given is a unit vector, which means,
Hence the angle between two vectors is . Correct option is B.
Question:12 Area of a rectangle having vertices A, B, C and D with position vectors
(A)1/2
(B) 1
(C) 2
(D) 4
Answer:
Given 4 vertices of rectangle are
Now,
Area of the Rectangle
Hence option C is correct.
Exercise 10.4 Class 12 Maths throughout explains about the cross products. The applications of cross products include finding the area of a triangle, parallelogram etc. Question number 9 of the Class 12th Maths chapter 10 exercise 10.4 is to find the area of a triangle. And questions 10 and 12 of NCERT Solutions for Class 12 Maths chapter 10 exercise 10.4 is to find the area of parallelogram and rectangle respectively.
Also Read | Vector Algebra Class 10 Chapter 10 Notes
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
The quantity that has magnitude and also direction is called a vector quantity.
A scalar quantity has magnitude only whereas a vector quantity has both magnitude and directions.
The value will be zero since the angle between them is zero. The cross product of two vectors a and b is absin(angle between them). For parallel vectors angle between them is zero. So sin(0)=0.
The direction of a cross b is opposite to the direction of b cross a. That is (a cross b)=-(b cross a)
No, stress is neither a vector nor a scalar. Stress is known as a tensor quantity.
It is a vector with magnitude=1
No, equal vectors may have different initial points, but the magnitude and directions of equal vectors will be the same.
The negative of a given vector is the vector with the same magnitude but opposite in direction.
Two or three questions from vector algebra can be expected for the CBSE Class 12 Maths board exam.
Vector algebra is used in almost all branches of engineering. If we consider electrical engineering, vector algebra is used to solve certain electromagnetic, power systems, electrical machines and power electronics problems.
Late Fee Application Date:22 July,2024 - 31 July,2024
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
Hello student,
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
Remember
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.
I hope this answer helps you. If you have more queries then feel free to share your questions with us, we will be happy to help you.
Good luck with your studies!
Hello Aspirant , Hope your doing great . As per your query , your eligible for JEE mains in the year of 2025 , Every candidate can appear for the JEE Main exam 6 times over three consecutive years . The JEE Main exam is held two times every year, in January and April.
Hi there,
Hope you are doing fine
Yes you are certainly eligible for giving the jee exam in the year 2025. You must pass the maths exam with at least 75% criteria as required by jee and provide the marksheet and the passing certificate while registering for the exam.
Pursuing maths as an additional subject while taking biology as your main subject does not offer any hindrance in you appearing for the jee examination. It is indeed an privilege to pursue both maths and biology as the subjects and prepare for the same.
There will be no issue in filling the form while registering for the exam as it will only require your basic details and marksheet which you can provide by attaching the marksheet of maths also. Also, a detailed roadmap is also available on the official websites on how to fill the registration form. So you can fill the form easily.
Hope this resolves your query.
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