Question

The vector that must be added to the vector i-3j-2k and 3i-6j+7k so that the resultant vector is a unit vector along y axis ! How to solve such problems?

Answer 1

We have :
A= i-3j+2k and B= 3i -6j+7k.

So here we want A+B+C= 1j. -(1) ( j is the unit vector along y axis)

So A+B = 4i - 9j +5k. - (2)

So by subst.( 2) in( 1) :

4i -9j +5k + C= j
C= j - ( 4i -9j +5k.)
= j -4i +10j -5k
= -4i +10j - 5k

Hence, -4i +10j -5k is the vector which must be added so that the resultant is a unit vector along y direction....

In these type of problems we first write, A+B+C=1×(direction of unit vector)

Then we add A&B.
The resultant of A+B is subtracted from 1×(direction of unit vector) .

So we get the desired vector.