3D Geometry
Vector 3D
nta_abhyas_2025
Grade 12
Question:
If the image of the point $(1, -2, 3)$ in the plane $2x + 3y - z = 7$ is the point $(\alpha, \beta, \gamma)$, then the value of $\alpha + \beta + \gamma$ is equal to
Step-by-Step Solution
Key Concept: Vector relationships and distance formulas in 3D space determine unknown parameters.
From the diagram showing points $P(2, 5, 1)$ and $R(6, 2a, 5)$ with $Q$ at $(0, 2c, 5)$, the condition $PQ - QR = 0$ (perpendicularity or equal distance property) is applied. Using vector calculations and the geometric relationships shown, the value is determined to be $\frac{1}{2}$.
Correct Answer: 3