Let the image of the point P(1,2,6) in the plane passing through the points A(1,2,0), B(1,…

Question

Let the image of the point $P(1,2,6)$ in the plane passing through the points $A(1,2,0),\ B(1,4,1),\ C(0,5,1)$ be $Q(\alpha,\beta,\gamma)$. Then $\alpha^2+\beta^2+\gamma^2$ is equal to:

Accepted Answer

Plane through $A,B,C$: $x+y-2z-3=0$.

Image of $(1,2,6)$: $\dfrac{\alpha-1}{1}=\dfrac{\beta-2}{1}=\dfrac{\gamma-6}{-2}=\dfrac{-2(1+2-12-3)}{6}=4$.
$$\alpha=5,\ \beta=6,\ \gamma=-2.$$
$$\alpha^2+\beta^2+\gamma^2=25+36+4=65.$$

Solutions · 1