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The equation of the line having equal inclinations with coordinate axes and passing through one point in line of intersection of the planes $2 x - y + z = 2 and x - y - z = - 1$

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$2 x = \frac{y}{2} = \frac{z}{3}$

$x = y = z$

$\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$

$\frac{x - 3}{1} = \frac{y - 4}{1} = \frac{z}{1}$

answer is D.

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Detailed Solution

Plug in $z = 0$ in the equations of two planes

the equations are $2 x - y = 2 and x - y = - 1$

Solving $x = 3, y = 4$

Therefore, the equation of the line passing through the point $(3, 4, 0)$ and making equal angles with coordinate axes is $\frac{x - 3}{1} = \frac{y - 4}{1} = \frac{z}{1}$

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