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 :