List of top Mathematics Questions on Distance of a Point from a Plane asked in KEAM

The distance between \( (2, 1, 0) \) and \( 2x + y + 2z + 5 = 0 \) is:

The straight line $\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(2\hat{i} + 5\hat{j} + 3\hat{k})$ is parallel to the plane $\vec{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = 5$. Then the distance between the straight line and the plane is:

The distance between the \( x \)-axis and the point \( (3, 12, 5) \) is:

The distance between the \( x \)-axis and the point \( (3, 12, 5) \) is:

The distance between the \( x \)-axis and the point \( (3, 12, 5) \) is: