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 Question 2.
Find \(\overrightarrow { a } \). \(\overrightarrow { b } \) , if \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are as follow :
Solution:
Exercise 13.2 Class 12 RBSE Question 3.
Prove that:
Solution:
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:
Exercise 13.2 Class 12 Question 5.
For which value of λ, vectors \(\overrightarrow { a } \) and \(\overrightarrow { b } \) are mutually perpendicular :
Solution:
Maths RBSE Solutions Class 12 Question 6.
Find the projection of the vector
on the vector
Solution:
12th Class RBSE Solution Question 7.
If
and
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 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,
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 Maths Question 10.
For any vector \(\overrightarrow { a } \), prove that
Solution:
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.
∴ 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.