## 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.

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