RBSE Solutions for Class 12 Maths Chapter 13 Vector Ex 13.5

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 12
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.

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