A ball is thrown upwards from the plane surface of the ground. Suppose the plane surface from which the ball is thrown also consists of the points A(1, 0, 2), B(3, -1, 1) and C(1, 2, 1) on it. The highest point of the ball takes, is D(2, 3, 1) as shown in the figure. Using this information answer the question.

The co-ordinates of the foot of the perpendicular drawn from the maximum height of the ball to the ground are

$\left(\frac{43}{29}, \frac{77}{29}, \frac{9}{29}\right)$

line perpendicular to plane

→  $\frac{x - 2}{3} = \frac{y-3}{2} = \frac{z-1}{4} = λ$

(x, y , z)

= (3λ + 2, 2λ + 3, 4λ + 1) points on line 

eq. of plane

→ 3x + 2y + 4z = 11 as foot of perpendicular lies both on line and plane

⇒  3(3λ + 2) + 2(2λ + 3) + 4(4λ + 1) = 11

9λ + 4λ + 16λ + 6 + 6 + 4 = 11 

29λ = -5

$λ = \frac{-5}{29}$

foot of perpendicular

(3λ + 2, 2λ + 3, 4λ + 1)

= $\left(\frac{43}{29}, \frac{77}{29}, \frac{9}{29}\right)$