Question

The co-ordinates of the foot of the perpendicular drawn from the point A (1, 0, 3) to the join of the points B (4, 7, 1) and

C(3, 5, 3) are –

• A. $\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)$
• B. (5, 7, 17)
• C. $\left( \frac{5}{7},\frac{- 7}{3},\frac{17}{3} \right)$ `
• D. $\left( –\frac{5}{3},\frac{7}{3},\frac{- 17}{3} \right)$

Answer 1

Answer: (A)

$\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)$

Answer 2

Let D be the foot of perpendicular and let it divides BC in the ratio l : 1. Then the co-ordinates of D are

$\frac{3\lambda + 4}{\lambda + 1}$, $\frac{5\lambda + 7}{\lambda + 1}$, $\frac{3\lambda + 1}{\lambda + 1}$

Now $\overset{\rightarrow}{AD}$ ^ $\overset{\rightarrow}{BC}$ = $\overset{\rightarrow}{AD}$.$\overset{\rightarrow}{BC}$ = 0

Ž – (2l + 3) – 2(5l + 7) – 4 = 0

Ž l = – $\frac{7}{4}$

\ Co-ordinates of D $\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)$