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Question
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
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Solution
Given `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then
`(1/2)^2 + (1/sqrt(2))^2 + "a"^2` = 1
`1/4 + 1/2 + "a"^2` = 1
`(1 + 2)/4 + "a"^2` = 1
a2 = `1 - 3/4`
= `(4 - 3)/4`
= `1/4`
a = `+- 1/2`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
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