List of top Mathematics Questions on Angle between a Line and a Plane asked in KEAM

If \( \alpha = \frac{\pi}{4} \), find \( (\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2 \).

If the line $\frac{x+1}{2} = \frac{y+1}{3} = \frac{z+1}{4}$ meets the plane $x + 2y + 3z = 14$ at $P$, then the distance between $P$ and the origin is:

The angle between the straight line \( \vec{r} = (\hat{i}+2\hat{j}+\hat{k}) + s(\hat{i}-\hat{j}+\hat{k}) \) and the plane \( \vec{r}\cdot(2\hat{i}-\hat{j}+\hat{k}) = 4 \) is

Foot of the perpendicular drawn from the origin to the plane \( 2x - 3y + 4z = 29 \) is:

Foot of the perpendicular drawn from the origin to the plane \( 2x - 3y + 4z = 29 \) is:

Foot of the perpendicular drawn from the origin to the plane \( 2x - 3y + 4z = 29 \) is:

The angle between the line $ \frac{3x-1}{3}=\frac{y+3}{-1} $ $ =\frac{5-2z}{4} $ and the plane $ 3x-3y-6z=10 $ is equal to