If a line makes angles 90^{\circ},135^{\circ},45^{\circ} with the x, y and z axes respectively, find its direction cosines. 

 

 

 

 
 
 
 
 

Answers (1)

Given  \alpha =90^{\circ},\beta =135^{\circ},\gamma =45^{\circ}

So, Direction cosines are    \alpha                  \beta                  \gamma           

                                         (\cos90^{\circ},\, \cos 135^{\circ},\, \cos 145^{\circ})

\cos 90=0,\, \cos 135=\cos(180-45)=\frac{1}{\sqrt{2}},\, \cos 45=\frac{1}{\sqrt{2}}

\Rightarrow \left ( 0,\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right )

 

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