Question

Vector A→, having magnitude 2.5m, pointing 37∘ south of east and vector B→ having magnitude 3.5m, pointing 20∘ north of east are added. What is the magnitude of the resultant vector?

Answer 1

Answer:

Magnitude of the resultant vector is R = 6.81 m

Explanation:

Given :

Vector A having magnitude of 2.5 m

Vector A having direction 37 degree south of east.

Vector B having magnitude of 3.5 m

Vector B having direction 20 degree north of east.

Therefore, the angle between the two vectors is, θ = 37+20 = 57 degree

So, the resultant of the two vectors are given by

$R = \sqrt{A^2+B^2+2AB \cos \theta}$

$R = \sqrt{2.5^2+3.5^2+2(2.5)(3.5) \cos 57}$

$R = \sqrt{6.25+12.25+17.5 \times 0.54}$

$R = \sqrt{46.45}$

R = 6.81 m