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RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

May 25, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2 are part of RBSE Solutions for Class 12 Maths. Here we have given Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.12.

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.2

Question 1.
If magnitude of two vectors be 4 and 5 units, then find scalar product of them, where angle between them be :
(i) 60°
(ii) 90°
(iii) 30°
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 2.
Find \(\overrightarrow { a } \). \(\overrightarrow { b } \) , if \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are as follow :
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 3.
Prove that:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 4.
If coordinates of P and Q are (3, 4) and (12, 4) respectively, then find ∠POQ where O is origin.
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 5.
For which value of λ, vectors \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are mutually perpendicular :
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 6.
Find the projection of the vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
on the vector
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 7.
If
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
and
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
then find a vector \(\overrightarrow { c } \), so that \(\overrightarrow { a } \), \(\overrightarrow { b } \), \(\overrightarrow { c } \) represents the sides of a right angled triangle.
Solution:
Given that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 8.
If | \(\overrightarrow { a } \) + \(\overrightarrow { b } \) | = | \(\overrightarrow { a } \) – \(\overrightarrow { b } \) |, then prove that \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are mutually perpendicular vectors.
Solution:
According to question,
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 9.
If coordinates of points A, B, C and D are (3, 2, 4), (4, 5, -1), (6, 3, 2) and (2, 1, 0) respectively, then prove that lines \(\overrightarrow { AB } \) and \(\overrightarrow { CD } \) are mutually erpendicular.
Solution:
Given that coordinates of points A, B, C and D are (3,2,4), (4,5,-1), (6,3,2) and (2,1,0) respectively.
Then position vectors of A, B, C and D with respect to origin are
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 10.
For any vector \(\overrightarrow { a } \), prove that
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
Solution:
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Question 11.
Use vectors to prove that sum of square of diagonal of a parallelogram is equal to the sum of square of their side.
Solution:
Let OACB is a parallelogram. Taking O as origin, the position vectors of A and B are \(\overrightarrow { a } \) and \(\overrightarrow { b } \) respectively.
RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2
∴ Sum of the squares of diagonals = sum of the squares of sides.
Hence the sum of square of diagonals of a parallelogram is equal to the sum of square of their sides.

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