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Question

If a line makes angles 90,135,45 with the positive X,Y and Z-axes respectively, find its direction cosines.


Solution

Let direction cosines of the line be l,m and n with the X,Y, and Z-axes respectively and given that

               α=90,β=135 and γ=45Then,            l=cosα=cos90=0,m=cosβ=cos135=1/2and               n=cosγ=cos45=1/2

Therefore, the direction cosines of the line are 0,12 and 12

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