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Question
Verify whether the following ratios are direction cosines of some vector or not
`1/5, 3/5, 4/5`
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Solution
The given ratios are l = `1/5`, m = `3/5`, n = `4/5`
l2 + m2 + n2 = `(1/5)^2 +(3/5)^2 + (4/5)^2`
= `1/25 + 9/25 + 16/25`
= `(1 + 9 + 16)/25`
= `26/25 ≠ 1`
If l, m, n are direction cosines of a vector then l2 + m2 + n2 = 1
∴ The given ratio `1/5, 3/5, 4/5` do not form the direction cosines of a vector.
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