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Question

# Vector A has a magnitude of 2 units and makes an angle of 0∘ with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of 30∘ (clock-wise) with the positive y- axis. Find the magnitude of the resultant of Vector A& B and also the angle that it makes with Vector A.

A

Magnitude =

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B

Magnitude =

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C

Magnitude =

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D

Magnitude =

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Solution

## The correct option is D Magnitude = By applying parallelogram law this can be made to look like Now we know magnitude of resultant is given by the formula √a2+b2+2ab cosθ So we hace √22+62+24 cos60∘=√52 Now we know to find the angle that it makes with the A vector we have the formula tanθ=b cosθ(a + bsinθ) tanθ=6 cos 60∘(2+6 sin 60∘)=3(2+3√3)

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