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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.
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
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.
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Here's why 2025 is more likely:
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hello,
Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.
I hope this was helpful!
Good Luck
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