3D Geometry
Image of Point in Line — Linear Combination
nta_pyq_2024_apr
Grade 12
Question:
Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(1,6,4)$ in the line $\dfrac{x}{1}=\dfrac{y-1}{2}=\dfrac{z-2}{3}$. Then $2\alpha+\beta+\gamma$ is equal to _____
Step-by-Step Solution
Key Concept: Foot $A=(t,2t+1,3t+2)$. $\overrightarrow{QA}\cdot(1,2,3)=0$: $(t-1)+2(2t-5)+3(3t-2)=0\Rightarrow14t=17\Rightarrow t=17/14$.
$2\alpha+\beta+\gamma=11$.
Correct Answer: 11