Question

1. A vector A makes an angle of 20° and B makes an angle
of 110° with the X-axis. The magnitudes of these vectors
are 3 m and 4 m respectively. Find the resultant.​

Answer 1

Answer:

SOLUTION::

Please see figure to understand the solution more nicely.

Angle made by vector A = 20°

Angle made by vector B = 110°

Angle between vector A and vector B = 110° - 20° = 90°

As given in question,

Magnitude of vector A , |A| = 3 m

Magnitude of vector B , |B| = 4 m

Resultant will be , R = √(A² + B²+2AB cosΘ) = 5 m

Let T be the angle between R vector and A vector.

T = tan⁻¹[(4sin90°)/(3 + 4cos90°)] = tan⁻1(4/3) = 53°

So, the resultant vector makes angle = (53° + 20°) = 73°

And also , 73° with respect to x-axis.

Hope it helps!