Question

A vector A is added to B=6 i – 8 j . The resultant vector is in the positive x direction and has a magnitude equal to A. Calculate the direction of A.

Answer 1

By adding B=6i-8i the restaurant then becomes (x+6)i + (y-8)j

The restaurant is in positive x direction which gives y=8

The magnitude of A and the restaurant are the same
x^2+y^2=(x+6)^2

12x=y^2-36=(8)^2-36=28
This gives x=7/3

Therefore vector A=(7/3) i +8j
The magnitude of A=sqrt [(7/3)^2+(8)^2]=25/3

A makes with positive x direction angle tan^(-1)
[8/(7/3)]
= tan^(-1) (24/7)

Hope this helps! :3