3D Geometry
Equal Distance from Plane — Distance from Line
nta_pyq_2023_apr
Grade 12
Question:
$\lambda_1,\lambda_2$ s.t. $(\frac{5}{2},1,\lambda)$ and $(-2,0,1)$ equidistant from $2x+3y-6z+7=0$. $\lambda_1>\lambda_2$. Distance of $(\lambda_1-\lambda_2,\lambda_2,\lambda_1)$ from line $\frac{x-1}{5}=\frac{y-2}{1}=\frac{z+7}{2}$ is ______
Step-by-Step Solution
Key Concept: Equidistant: $|2(5/2)+3(1)-6\lambda+7|=|2(-2)+3(0)-6(1)+7|$ gives two values for $\lambda$.
Distance $=9$.
Correct Answer: 9