Question

Statement $1$: There exist two points on the line $\frac{x-1}{1}=\frac{y}{-1}=\frac{z+2}{2}$ which are at a distance of $2$ units from point $(1,2,-4)$.

Statement $2$: Perpendicular distance of point $(1,2,-4)$ from the line $\frac{x-1}{1}=\frac{y}{-1}=\frac{z+2}{2}$ is $1$ unit.

• A. Both the statements are true, and Statement $2$ is the correct explanation for Statement $1$.
• B. Both the statements are true, but Statement $2$ is not the correct explanation for Statement $1$.
• C. Statement $1$ is true and Statement $2$ is false.
• D. Statement $1$ is false and Statement $2$ is true.

Answer 1

The correct option is C Statement $1$ is true and Statement $2$ is false.

Given line $\frac{x-1}{1}=\frac{y}{-1}=\frac{z+2}{2}$ and point$(1,2,-4)$

Projection of $AB$ on the line $1\left(0\right)-1\left(2\right)+2(-2)=-p$

$AP=\sqrt{{AB}^2+{PB}^2}$