Question

The resultant of two vectors at an angle 150° is 10
units and is perpendicular to one vector. The
magnitude of the smaller vector is
(1) 10 units
(2) 10/3 units
(3) 10/2 units
(4) 513 units​

Answer 1

Explanation:

On the off chance that we draw the resultant vector from the starting point along x-axis:

one of the vectors is Perpendicular to resultant vector, so check vector a from the starting point along +y axis.

From the graph, we can tell that the other vector b at 150 degrees clockwise from vector an(i.e 60 degrees from +X axis)

IN X direction,b.cos60° =10

since cos60°=1/2

b=10/1/2=20

in the Y direction:

a=b.sin60°

since sin 60°=√ 3/2

a=20 √ 3/2

=10√3

Since 10√3 is smaller than 20. hence answer is 10√3

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