Question

Perpendicular distance of point (1, 2, 3) from the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ is

• A. 8
• B. 6
• C. 7
• D. 5

Answer 1

Answer: (D)

5

Answer 2

$\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2} = \lambda$

\ x = 3l + 6, y = 2l + 7, z = – 2 l + 7

\ M(3l + 6, 2l + 7, –2 l + 7)

\ D.R's of PM are 3l + 6 – 1, 2l + 7 – 2, –2l + 7 – 3

3l + 5, 2l + 5, –2l + 4

D.R's of line are 3 , 2, – 2

Both PM and line are perpendicular therefore

3(3l + 5) + 2(2l + 5) – 2(–2l + 4) = 0

̃ l= –1

\ PM = 7