# Vector Product (Part-4) | S N Dey | Class 12

In the previous article we have discussed 11 Short Answer Type Questions and their solutions of Vector Product . In this article, we will discuss the solutions of Short Answer Type Questions (12-22) in the chapter Product of Two Vectors as given in the Chhaya Publication Book of aforementioned chapter of S N De book. To download S N dey mathematics class 12 PDF, you can check out here. So, without wasting time, let’s start.

##### Vector Product | S N Dey mathematics class 12 Solutions of Ex-2A

Let be three given vectors.

Find

Solution.

Find

Solution.

Find

Solution.

Find

Solution.

Find angle between

Solution.

If be the angle between

Find sine of the angle between

Solution.

We have

In each of the following find a unit vector perpendicular to both

Solution.

So, a unit vector perpendicular to both is :

Solution.

So, a unit vector perpendicular to both is :

Solution.

So, a unit vector perpendicular to both is :

If show that,

Solution.

So, by we get,

Hence , by the result follows.

Solution.

So, by we get,

Hence , by the result follows.

By vector method show that the points are collinear.

Solution.

Hence, by we get,

So, by we can conclude that three given points are collinear.

If find a vector of magnitude perpendicular to both

Solution.

So, a vector of magnitude perpendicular to both is :

If and find the cosine of the angle between the vectors

Solution.

If is the angle between then

Prove that,

Solution.

Note [*] :

Solution.

Solution.

Given that and What can you conclude about the vector ?

Solution.

If possible let

Hence , the value of obtained from and are contradictory to each other and so our assumption is wrong and so either

If show that,

Solution.

Hence by we get,

Find the value of

Solution.

We know,

Find a unit vector perpendicular to both the vectors and

Solution.

Clearly, is a vector which is perpendicular to both

So, a unit vector perpendicular to both the given vectors is given by :

Find a unit vector perpendicular to each of the vectors where

Solution.

From we get

So, a unit vector perpendicular to each of the vectors

is given by :