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Question

Which of the following is/are a unit vector for all values of θ ?

A
(cosθ)^i(sinθ)^j
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B
(sinθ)^i+(cosθ)^j
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C
(sin2θ)^i(cosθ)^j
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D
(cos2θ)^i(sin2θ)^j
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Solution

The correct option is D (cos2θ)^i(sin2θ)^j
We know, unit vector has magnitude equal to 1.

a:(cosθ)^i(sinθ)^j
magnitude=cos2θ+sin2θ=1 θR
So, a unit vector.

b:(sinθ)^i+(cosθ)^j
magnitude=sin2θ+cos2θ=1 θR
So, a unit vector.

c:(sin2θ)^i(cosθ)^j
magnitude=sin22θ+cos2θ1 for all θR
so, not a unit vector.

d:(cos2θ)^i(sin2θ)^j
magnitude=cos22θ+sin22θ=1 θR
so, a unit vector.

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