Question

Hello guys, please help me with this : How many unit vectors are there for which cos alpha = 1/2 and cos beta = 1/2, where alpha and beta are angles made with x-axis and y-axis respectively.

Answer 1

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ANSWER

direction cosines relation -

cos

2

α+cos

2

β+cos

2

γ=1

1−sin

2

α+1−sin

2

β+1−sin

2

γ=1

⇒sin

2

α+sin

2

β+sin

2

γ=3−1=2

∴

sin

2

α+sin

2

β+sin

2

γ=2

Answer 2

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