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