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Question
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
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Solution
The given ratios are l = `4/3`, m = 0, n = `3/4`
l2 + m2 + n2 = `(4/3)^2 + 0^2 + (3/4)^2`
= `16/9 + 0 + 9/16`
= `(16 xx 16 + 9 xx 9)/(9 xx 16)`
= `(256 + 81)/144 ≠ 1`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio do not form the direction cosines of a vector.
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