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

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Solution

Let, the unit vector in XY plane be a → , then,

a → =cosθ i ^ +sinθ j ^ (1)

Since θ is the angle with the positive direction of x-axis that is made by the unit vector, then θ=30°.

Substitute θ=30° in equation (1).

a → =cos30 i ^ +sin30 j ^ = 3 2 i ^ + 1 2 j ^

Therefore, the unit vector is 3 2 i ^ + 1 2 j ^ .

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