Question

If $P(x,y,z)$ moves such that $x=0,z=0$, then the locus of $P$ is the line whose d.cs are

• A. $y$-axis
• B. $1,0,0$
• C. $0,1,0$
• D. $0,0,0$

Answer 1

The correct option is C $0,1,0$

When $P$ moves then $x=0,z=0$ but $y$ is not given.

Let $y=y$

Then the coordinates of the point will be $(0,y,0)$

Now, direction cosines with respect to $(0,y,0)$ is given by

$\cos \alpha =\frac{0}{\sqrt{0^2+y^2+0^2}}=\frac{0}{y}=0$
$\cos \beta =\frac{y}{\sqrt{0^2+y^2+0^2}}=\frac{y}{y}=1$
$\cos \gamma =\frac{0}{\sqrt{0^2+y^2+0^2}}=\frac{0}{y}=0$
Hence, the direction cosines are $0,1,0$.