Question

A VectorA is added to B=6i-8j the resultant vector is in the positive x direction and has a magnitude equal to A CALCULATE the direction of A

Answer 1

Let

$$\bold{A}=x\bold{i}+y\bold{j}$$

$$\bold{A+B}=(x+6)\bold{i}+(y-8)\bold{j}=z\bold{i}$$

$$y=8, x+6=z$$

But

$$|\bold{A}|=|\bold{A+B}|\to z^2=x^2+y^2$$

$$(x+6)^2=x^2+8^2$$

$$x=\frac{7}{3}$$

The direction of A is

$$\theta=\arctan{\frac{y}{x}}=\arctan{\frac{8}{\frac{7}{3}}}=73.7\degree$$

counterclockwise from the positive x direction.