Question

Through the point P(1,2,2,) a plane is drawn at right angles to OP, O being the origin, to meet the axes in A, B, C. If the area of triangle ABC is $\frac{402+\lambda }{8}$ then $\lambda$ is___

Answer 1

Equation of plane through P is x + 2y + 2z = 9
$A=(9,0,0),B=(0,\frac{9}{2},0)C=(0,0,\frac{9}{2})$
$Area=\frac{1}{2}|\overrightarrow{AB}\times \overrightarrow{AC}|=\frac{1}{2}\sqrt{{\overline{AB}}^2{\overline{AC}}^2-(\overline{AB}-\overline{AC}{)}^2}=\frac{405}{8}=\frac{402+\lambda }{8}or\lambda =3$