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Question
Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of the x-axis.
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Solution
Let OP lie in XY - plane so that ∠XOP = 30°, ∠POY = 60° and ∠POZ = 90°
∴ The direction cosines of OP are
< cos 30°, cos 60°, cos 90°>
i.e., `< sqrt3/2, 1/2, 0>`
∴ `vec(OP) = sqrt3/2 hati + 1/2 hatj`
Now,
`|vec(OP) = sqrt((sqrt3/2)^2 + (1/2)^2)|`
`= sqrt(3/4 + 1/4)`
`= sqrt1`
= 1
Hence the required vectors is `sqrt3/2 hati + 1/2 hatj`
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