Vectors Problem Example 1

Description:

Problem

A vector a→ makes an angle of 20^o and b→ makes an angle of 110^o with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.

Solution

Now, taking the vectors separately and adding them using Parallelogram Law −

Now, using the formulae for magnitude and direction of the resultant −

|R→| = √|a→|² + |b→|² + 2|a→||b→| cos90^o = 5m

tan α = |b→| sinθ/|a→| + |b→| cosθ = 4sin 90^o/3 + 4cos 90^o = 4/3 ⇒ α = tan^-14/3

The resultant, R→, makes an angle of (α + 20^o) with the X − axis.