NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 contains all the questions with detailed solutions. Students are advised to solve these questions for better understanding of the concepts in exercise 10.2.
Krati Saraswat13 Feb, 2024
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NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 (Vector Algebra)
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 Vector Algebra is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 10. Given below are step-by-step solutions to all questions given in the NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2.NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 Overview
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 cover several important topics. It is highly recommended for students to review each topic thoroughly in order to gain a comprehensive understanding of the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the result of dedicated efforts by the Physics Wallah teachers aimed at assisting students in grasping the concepts covered in this chapter. By going through and practicing these solutions, the objective is for students to achieve excellent results in their exams effortlessly.NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2: Question 1. Compute the magnitude of the following vectors:
Solution :
The given vectors are:
Hence, and are two different vectors having the same magnitude. The vectors are different because they have different directions.
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NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1
Question 3. Write two different vectors having same direction. Solution :
The direction cosines of and are the same. Hence, the two vectors have the same direction.
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3
Question4
.
Find the values of
x
and
y
so that the vectors
are equal
will be equal if their corresponding components are equal.
Hence, the required values of
x
and
y
are 2 and 3 respectively.
Question
5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
Solution :
The vector with the initial point P (2, 1) and terminal point Q (–5, 7) can be given by,
Hence, the required scalar components are –7 and 6 while the vector components are
Question
6. Find the sum of the vectors:
Solution :
Given:
Question
7. Find the unit vector in the direction of the vector
Solution :
The unit vector in the direction of vector
is given by = / |a|
.png)
Question
8. Find the unit vector in the direction of the vector
where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.
Solution :
Given: Points P (1, 2, 3) and Q (4, 5, 6)
Hence, the unit vector in the direction of
is
Question
9. For given vectors
find the unit vector in the direction of +
.png)
.png)
Solution :
Given: Vectors
Hence, the unit vector in the direction of (
+ )
is
Question
10. Find the vector in the direction of vector which has magnitude 8 units.
Solution :
Let
=
Hence, the vector in the direction of vector
which has magnitude 8 units is given by,
Question
11. Show that the vectors are collinear.
Solution :
Let
= λ
where λ = 2
Hence, the given vectors are collinear.
Question
12. Find the direction cosines of the vector
Solution :
The given vector is =
We know that the direction cosines of a vector
are coefficients of
Question
13. Find the direction cosines of the vector joining the points A (1, 2, –3) and
B (–1, –2, 1) directed from A to B.
Solution :
The given points are A (1, 2, –3) and B (–1, –2, 1).
Question
14. Show that the vector
is equally inclined to the axes OX, OY and OZ.
Solution :
Let =
Hence, the given vector is equally inclined to axes OX, OY, and OZ.
Question
15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are
and -
respectively, in the ratio 2 : 1
(i) internally
(ii) externally.
Solution :
The position vector of point R dividing the line segment joining two points
P and Q in the ratio
m:
n
is given by
(i) Internally:
=
(ii) Externally:
=
Position vectors of P and Q are given as:
Question
16. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q
(4, 1, – 2).
Solution :
The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, – 2) is given by,
Question
17. Show that the points A, B and C with position vectors
respectively form the vertices of a right angled triangle.
Solution :
Position vectors of points A, B, and C are respectively given as:
Hence, ABC is a right-angled triangle.
Question
18. In triangle ABC (Fig. below), which of the following is not true:
Solution :
Hence, the equation given in alternative C is
incorrect
.
The correct answer is
C.
Question
19. If
and
are two collinear vectors, then which of the following are incorrect:
(A)
= λ
for some scalar λ
(B) = ±
(C) The respective components of
and
are proportional.
(D) Both the vectors
and
have same direction, but different magnitudes.
Solution :
Option (D) is not true because two collinear vectors can have different directions and also different magnitudes.
The option (A) and option (C) are true by definition of collinear vectors.
Option (B) is a particular case of option (A).
NCERT Solutions For Class 12 Maths Chapter 10 Exercise 10.2 FAQs
How many exercises are there in vector algebra?
NCERT Solutions Class 12 Maths Chapter 10 Vector Algebra has a total of 63 questions that have been spread across 5 exercises including a miscellaneous one.
What is a vector in 12th maths?
Vector Algebra for class 12 is all about the study of vectors and scalars. There are various quantities, which involves magnitude as well as direction. If the quantity that has magnitude, as well as direction, is known as vectors. Such quantities are known as Vector Quantities.
Who invented vector algebra?
Vector calculus and its sub objective Vector Fields was invented by two men J. Willard Gibbs and Oliver Heaviside at the end of the 19th century.
What is vector rule?
The triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the triangle's third side represents the direction and the magnitude of the resultant vector.
How do vectors work?
A vector is an object that has both a magnitude and a direction.
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