Question

. A vector A and B makes angles 30° and 120°
respectively with the positive X-axis. The
magnitude of these vectors are 5m and 12m
respectively. The |A + B =​

Answer 1

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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.