NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3 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 10.3 Overview
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3 Vector Algebra is prepared by the academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of Chapter 10. Below are step-by-step solutions to all questions given in the NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3.NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3 Overview
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3 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 10.3
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.3: Question 1. Find the angle between two vectors.png)
and
.png)
with magnitude √3 and 2 respectively having
.
= √6
Solution :
It is given that,
Hence, the angle between the given vectors
and
is π/4.
.
Solution :
The given vectors are
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.1
Question 3. Find the projection of the vector
on the vector
Solution :
Let
=
and
=
Now, projection of vector
on
is given by,
Hence, the projection of vector
on
is 0.
Question
4. Find the projection of the vector
on the vector
Solution :
Let
=
and
=
Now, projection of vector
on
is given by,
NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2
Question 5. Show that each of the given three vectors is a unit vector:
Also show that they are mutually perpendicular to each other.
Solution :
Hence, the given three vectors are mutually perpendicular to each other.
Question
6. Find
Solution :
Question
7. Evaluate the product
Solution :
Question
8. Find the magnitude of two vectors
and
having the same magnitude such that the angle between them is 60° and their scalar product is 1/2.
Solution :
Let
θ
be the angle between the vectors
and
Question
9. Find
if for a unit vector
.
Solution :
Question
10. If
are such that
+ λ
is perpendicular to
.png)
then find the value of λ
Solution :
Given:
Question
11. Show that
is perpendicular to
for any two non-zero vectors
and
Solution :
Question
12. If and
.
= 0 and
.
= 0 , then what can be concluded about the vector
?
Solution :
It is given that
.
= 0 and
.
= 0 .
Hence, vector
satisfying
.
= 0can be any vector.
Question
13. If
,
and
are unit vectors such that
+
+
= 0 find the value of
Solution :
Since,
+
+
= 0
are unit vectors.
Question
14. If either vector
. But the converse need not be true. Justify your answer with an example.
Solution :
Hence, the converse of the given statement need not be true.
Question
15.
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors
]
Solution :
The vertices of ΔABC are given as A (1, 2, 3), B (–1, 0, 0), and C (0, 1, 2).
Also, it is given that ∠ABC is the angle between the vectors
.
Question
16.
Show that the points A (1, 2, 7), B (2, 6, 3) and C (3, 10, –1) are collinear.
Solution :
The given points are A (1, 2, 7), B (2, 6, 3), and C (3, 10, –1).
Hence, the given points A, B, and C are collinear.
Question
17. Show that the vectors
form the vertices of a right angled triangle.
Solution :
Let vectors
be position vectors of points A, B, and C respectively.
Hence, ΔABC is a right-angled triangle.
Question
18.
If
is a nonzero vector of magnitude ‘
a
’ and λ a nonzero scalar, then
λ
is unit vector if
(A) λ = 1
(
B) λ = –1
(C) a = |
λ
|
(D) a = 1/|
λ|
Solution :
Therefore, option (D) is correct.
NCERT Solutions For Class 12 Maths Chapter 10 Exercise 10.3 FAQs
What topics are covered in Exercise 10.3 of Chapter 10 in Class 12 Maths?
Exercise 10.3 of Chapter 10 in Class 12 Maths covers topics related to the evaluation of integrals using the method of substitution, including trigonometric integrals and integrals involving exponential and logarithmic functions.
Are the NCERT Solutions for Exercise 10.3 of Chapter 10 in Class 12 Maths helpful for exam preparation?
Yes, the NCERT Solutions for Exercise 10.3 of Chapter 10 in Class 12 Maths are immensely helpful for exam preparation. They provide step-by-step explanations and solutions to the questions, helping students understand the concepts thoroughly and practice effectively for exams.
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.
Is vectors class 12 easy?
Vector Algebra is a moderately difficult chapter in CBSE Class 12 mathematics that can be scoring if students prepare it thoroughly. Science students have an advantage as they become familiar with the concepts of vectors in Class 11 physics.
Is vector algebra easy?
Vector algebra is much easier to apply than geometry and requires knowledge of fewer rules.
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