Question

A=4i+3j B=2i+5j
What is the equation of the resultant vector?
What angle does it make with respect to the x axis?

Answer 1

so, resultant means what in this case? are we adding, subtracting, multiplying?

Answer 2

C?

Answer 3

...? that makes no sense

Answer 4

I think when we graph those vectors there's a resultant which would be C

Answer 5

so adding?

Answer 6

you are taking two object and talking about a result. Well, we need to know for what operation. I am guessing that we are talking about vector addition, but maybe not?

Answer 7

If, indeed they mean addition, then you add the like parts.

\(A+B = 4i+3j+2i+5j=4i+2i+3j+5j=(4+2)i+(3+5)j=6i+8j\).

To get the angle we note that \(\tan(\theta)=\frac{\text{rise}}{\text{run}}=\frac{8}{6}\implies \theta = \tan^{-1}(\frac{4}{3})\approx53.13^{\circ}\)