3D Geometry
Distance Along a Given Line to Line L
nta_pyq_2024_apr
Grade 12
Question:
Consider the line $L$ passing through the points $(1,2,3)$ and $(2,3,5)$. The distance of the point $\left(\dfrac{11}{3},\dfrac{11}{3},\dfrac{19}{3}\right)$ from the line $L$ along the line $\dfrac{3x-11}{2}=\dfrac{3y-11}{1}=\dfrac{3z-19}{2}$ is equal to:
Step-by-Step Solution
Key Concept: Line $L$: direction $(1,1,2)$, through $(1,2,3)$. Given line through $A(11/3,11/3,19/3)$ with direction $(2,1,2)$. Find $B$ (intersection of given line with $L$): $B=(1+\lambda,2+\lambda,3+2\lambda)$. $B$ on given line: DRs $(B-A)\propto(2,1,2)$.
$B=(5/3,8/3,13/3)$. $AB=3$.
Correct Answer: 4