Three Dimensional Geometry

Which of the following lines is parallel to the line with direction ratios $(1, -2, 3)$?

If $(a, b, c)$ are direction ratios of a line, then which of the following is also a set of direction ratios for the same line?

If a point $P$ is at a distance $r$ from the origin and the direction cosines of $OP$ are $(l, m, n)$, then the $x$-coordinate of $P$ is:

If $(\frac{1}{2}, \frac{1}{2}, n)$ are the direction cosines of a line, then the value of $n$ is:

What is the direction ratio of a line passing through $(2, 3, 4)$ and $(5, 6, 7)$?

Find the direction ratios of the line $\frac{x-2}{3} = 2y-1 = z$.

If two lines are $\vec{r} = \vec{a}_1 + \lambda \vec{b}_1$ and $\vec{r} = \vec{a}_2 + \mu \vec{b}_2$, the vector representing the displacement between points on the two lines is generally:

The direction ratios of a line passing through $(0,0,0)$ and $(1,2,3)$ are:

Find the shortest distance between the lines $x=1, y=1$ and $x=4, y=5$ in 3D.

The equation of the plane passing through $(2, 3, 4)$ and perpendicular to the $z$-axis is:

The vector equation of the plane $3x - 4z = 12$ is:

If a plane passes through $(k, 0, 0)$, $(0, k, 0)$, and $(0, 0, k)$, its equation is:

The sine of the angle between the plane $x + y + z = 1$ and the line joining $(0,0,0)$ and $(1,2,3)$ is:

If $A(1,0,0)$, $B(0,1,0)$, and $C(0,0,1)$ are points, the angle between the lines $AB$ and $AC$ is:

The angle between the planes $x = 2$ and $y = 3$ is:

Find the distance of the point $(3, 4, 5)$ from the plane $2x - y + 2z = 3$.

Find the distance of the point $(1, 1, 1)$ from the plane $4x + 3y + 12z = 6$.

The distance of the point $(4, -2, 3)$ from the plane $2x - 2y + z = 5$ is: