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Question

Write down a unit vector in XY- plane, making an angle of 30 with the positive direction of xaxis .

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Solution

If r is a unit vector in the XYplane, then r=cosθ^i+sinθ^j.
Here, θ is the angle made by the unit vector with the positive direction of the xaxis
Therefore, for θ=30:
r=cos30+sin30^j=32^i+12^j
Hence, the required unit vector is 32^i+12^j.

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