The equation of plane that contains line $\frac{x - 1}{-1} = \frac{y + 1}{2} = \frac{z - 1}{3}$ and also pass through point $(0, 1, 0)$ is :

If a line makes angles α, β and γ with positive x-axis, y-axis and z-axis respectively, then the value of

$sin^2\frac{α}{2}cos^2\frac{α}{2} + sin^2\frac{β}{2}cos^2\frac{β}{2} + sin^2\frac{γ}{2}cos^2\frac{γ}{2}$ is

The equation of the plane, parallel to the plane $3x + 4y - 12z = 3$ and passes through $(1, 1, -1)$, is :

The shortest distance between the lines $\dfrac{x+1}{7}=\dfrac{-y-1}{6}=\dfrac{z+1}{1}$ and $\dfrac{x-3}{1}=\dfrac{-y+5}{2}=\dfrac{z-7}{1}$ is

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2) respectively, then the angle between the lines AB and CD is

The acute angle between the lines $\vec{r} = (4\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{j} - 3\hat{k})$ and $\frac{x-1}{1} = \frac{y+1}{-3} = \frac{z-2}{2}$ is

A line passes through the point with position vector $2\hat{i} - \hat{j} + 4\hat{k}$ and is in the direction of the vector $\hat{i} + \hat{j} - 2\hat{k}$. The equation of the line in Cartesian form is: