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  • Need explanation for: A line makes equal angles with co-ordinate axes. Direction cosine of this line are

A line makes equal angles with co-ordinate axes. Direction cosine of this line are

  • Option 1)

    ^+_-1,^+_-1,^+_-1

  • Option 2)

    ^+_-\frac{1}{\sqrt3}, ^+_-\frac{1}{\sqrt3}, ^+_-\frac{1}{\sqrt3}

  • Option 3)

    ^+_-\frac{1}{3}, ^+_-\frac{1}{3}, ^+_-\frac{1}{3}

  • Option 4)

    ^+_-\sqrt3, ^+_-\sqrt3, ^+_-\sqrt3

 

Answers (1)

best_answer

As learnt in

Direction Cosines -

If \alpha, \beta, \gamma are the angles which a vector makes with positive X-axis,Y-axis and Z-axis respectively then\cos \alpha, \cos \beta, \cos \gamma are known as diresction cosines, generally denoted by (l,m,n).

l=\cos \alpha, m=\cos \beta, n=\cos \gamma

l^{2}+m^{2}+n^{2}= 1

\cos^{2} \alpha+ \cos^{2} \beta+\cos^{2} \gamma= 1

- wherein

 

 \cos ^{2}\alpha +\cos ^{2}\beta +\cos ^{2}\gamma = 1                             where, \alpha =\beta =\gamma

\Rightarrow 3\cos ^{2}\alpha =1

\Rightarrow \cos ^{2}\alpha =\frac{1}{3}\ \Rightarrow \cos \alpha = \pm \frac{1}{\sqrt{3}}


Option 1)

^+_-1,^+_-1,^+_-1

This option is incorrect

Option 2)

^+_-\frac{1}{\sqrt3}, ^+_-\frac{1}{\sqrt3}, ^+_-\frac{1}{\sqrt3}

This option is correct

Option 3)

^+_-\frac{1}{3}, ^+_-\frac{1}{3}, ^+_-\frac{1}{3}

This option is incorrect

Option 4)

^+_-\sqrt3, ^+_-\sqrt3, ^+_-\sqrt3

This option is incorrect

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