Question

Find the magnitude and direction of the vector. Round the length to the nearest tenth and the degree to the nearest unit. Diagram is not drawn to scale.

Answer 1

The diagram shows the coordinates of the vector. They are:

East-coordinate = 6

North-coordintate = 4

A) To find the magnitude you just use Pythagorean theorem:

c^2 = 6^2 + 4^2 = 36 + 16 = 52 => c = √52 = 7.21

7.21 rounded to the nearest tenth is 7.2

B) To find the direction find the angle using trigonometric ratios:

tan(angle) = 4/6 = 2/3 => angle = arctan(2/3) = 33.69 degrees

That is 33.69 degrees North of East, which is written N 33.69° E