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Question

If a line makes angles α,β, γ with the coordinate axes, then


A

cos2α+cos2β+cos2γ1=0

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B

cos2α+cos2β+cos2γ2=0

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C

cos2α+cos2β+cos2γ+1=0

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D

cos2α+cos2β+cos2γ+2=0

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Solution

The correct option is C

cos2α+cos2β+cos2γ+1=0


Explanation for the correct option:

Given, The line makes angles α,β and γ with coordinate axis

l2+m2+n2=1

cos2α+cos2β+cos2γ=1 ….(1)

Now,

cos2α+cos2β+cos2γ=2cos2α-1+2cos2β-1+2cos2γ-1=2cos2α+cos2β+cos2γ-3=21-3=-1

cos2α+cos2β+cos2γ+1=0

Hence, Option ‘C’ is Correct.


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