RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

Rajasthan Board RBSE Class 12 Maths Chapter 13 Vector Ex 13.5

Question 1.
Find the value of


Solution:

Question 2.
Prove that

Solution:

Question 3.
Evaluate the formula

Solution:

Question 4.
For any vector , prove that:

Solution:
We know that

Question 5.
Prove that

Solution:

Question 6.
Prove that ,, are coplanar if × , × , × [/latex], are coplanar
Solution:

Question 7.
Prove that

Solution:

Question 8.
If magnitude of two and are √3 and 2 respectively  and. = √6, then find the angle between and
Solution:

Question 9.
Find the angle between the vectors

and

Solution:

Question 10.
Find the projection of vector

Solution:

Question 11.
Find projection vector on vector

on vector

Solution:

Question 12.
Find the value of

Solution:

Question 13.
Find the magnitude of two vectors and , if their magnitude are equal and angle between them is 60° and their scalar product is
Solution:
According to question

Question 14.
If for a vector , ( – ).( + ) = 12, then | |.
Solution:
According to question,

Question 15.

such that + λ is perpendicular on , then find the value of λ.
Solution:
According to question + λ is a perpendicular to

Question 16.
If vertices , , are such that
+ + =
then, find the value of . + . + .
Solution:
According to question

Question 17.
If vectors/1, B, C of triangle ABC are (1, 2,3), (-1,0, 0,), (0, 1, 2) respectively, then find ∠ABC.
Solution:
Let O be the origin.

RBSE Solutions for Class 12 Maths