RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.2

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.2

RBSE Solutions For Class 12 Maths Chapter 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 13.2
RBSE Solutions For Class 12 Maths Chapter 13

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

Exercise 13.2 Class 12 RBSE Question 3.
Prove that:
Maths RBSE Solutions Class 12 Chapter 13
Solution:
12th Class RBSE Solution Chapter 13
RBSE Solution 12th Class Chapter 13

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

RBSE Solution Class 12th Maths Chapter 13

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

Maths RBSE Solutions Class 12 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 Physics Class 12 Chapter 13
RBSE Solution Class 12 Physics Chapter 13

12th Class RBSE Solution 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 Solution Physics Class 12 Chapter 13
RBSE Solution Of Class 12th Chapter 13

RBSE Solution 12th Class 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,
Physics Class 12 RBSE Solutions Chapter 13

RBSE Solution Class 12th English 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 Solution Class 12th Physics Chapter 13
RBSE Solutions 12 Maths Chapter 13

RBSE Solution Class 12th Maths 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

RBSE Solutions Of Class 12 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.

RBSE Solutions for Class 12 Maths