Equation of line passing through origin and ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 7 of 20

Marks: +1, -0

Equation of line passing through origin and making

30^{\circ} , 60^{\circ}

and

90^{\circ}

with x, y, z axes respectively is:

Solution:

Direction cosines is given by

(\cos \alpha, \cos \beta, \cos \gamma) \equiv (\cos 30^{\circ}, \cos 60^{\circ}, \cos 90^{\circ}) \equiv \left(\;\frac{\sqrt{3}}{2}, \;\frac{1}{2}, 0\right)

Equation of the line is:

\;\frac{x-0}{\frac{\sqrt{3}}{2}} = \;\frac{y-0}{\frac{1}{2}} = \;\frac{z-0}{0}

\Rightarrow \;\frac{2x}{\sqrt{3}} = \;\frac{2y}{1} = \;\frac{z}{0}

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