Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The equations of the first line are $x=y,z=0$.

This can be written in symmetric form as $\frac{x}{1}=\frac{y}{1}=\frac{z}{0}$.

The direction ratios of the first line are $(1,1,0)$.

The equations of the second line are $y=0,z=0$.

This represents the x-axis, which can be written as $\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$.

The direction ratios of the second line are $(1,0,0)$.

Let $\theta$ be the angle between the two lines. Then,

$\cos \theta =\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}$

$\cos \theta =\frac{1(1)+1(0)+0(0)}{\sqrt{1^2+1^2+0^2}\sqrt{1^2+0^2+0^2}}$

$\cos \theta =\frac{1}{\sqrt{2}}$

$\theta =45^{\circ }$

Answer: $45^{\circ }$