Question

A Plane x + 2y – 3z = 12 has point P which is at minimum distance from the line joining

A(1, 0, –3) and B(2, 3, –1) then AP² is equal to –

• A. 0
• B. 14
• C. 28
• D. 56

Answer 1

Answer: (D)

56

Answer 2

Equation of line AB : = = $\frac { \mathrm { z } + 3 } { \mathrm { z } }$

Ž Any point on the line is (l + 1, 3l, 2l – 3)

It lie's on the plane

So (l + 1) + 2 (3l) – 3(2l – 3) = 12

Ž l = 2

Ž P (3, 6, 1)

\ AP² = 4 + 36 + 16 = 56