Find the acute angle made by vector $OC$ and the x-axis.

Question

Given that vector $OA$ = $3i+5j$, $OB$ = $-2i+6j$ and that $OC$ = $OA + OB$, calculate

i) |OC|,

ii) the acute angle made by vector $OC$ and the x-axis.

I found i) $\sqrt122$

Please help me in finding the answer to ii).

Answer 1

$OC$ = $OA + OB =3i+5j + -2i+6j = i+11j $

ii) the acute angle made by vector $OC$ and the x-axis.

Use $ a\cdot b = |a||b|cos\theta$

Set $a = OC $and $b = i$ for angle with x-axis