Question

A vector of magnitude 30 and direction eastwards is added with another vector of magnitude 40 and direction northwards . find the magnitude and direction of resultant with the east.

Answer 1

Resultant vector = 30i + 40j
Magnitude = √(30² + 40²)
= 50

Direction
Tanθ = 40/30 = 4/3
θ = 37° with East

Answer 2

Resultant vector = 30 i^ + 40 j^
= √30^2 + 40^2
=√900 + 1600
=√2500 = 50 (MAGNITUDE)

For direction,
$\tan( \alpha ) = \frac{perpendicuar}{ base} \\ \tan( \alpha ) = \frac{40}{30} = \frac{4}{3} \\ \alpha = 53 \: degree$
therefore, the direction will be 53° east.