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Question
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
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Solution
Given, a = –18, b = 12, c = –4
∴ `sqrt(a^2 + b^2 + c^2)`
= `sqrt((-18)^2 + (12)^2 + (-4)^2)`
= `sqrt(324 + 144 + 16)`
= `sqrt484`
= 22
Let a, b, c be direction ratios, then direction cosine is given by,
∴ cos α = `a/sqrt(a^2 + b^2 + c^2)`
= `(-18)/22`
= `(-9)/11`
cos β = `b/sqrt(a^2 + b^2 + c^2)`
= `12/22`
= `6/11`
cos γ = `c/sqrt(a^2 + b^2 + c^2)`
= `(-4)/22`
= `(-2)/11`
Hence, the direction cosines of the line are `(-9)/11, 6/11` and `(-2)/11`.
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