Question

If p₁and p₂ are the lengths of the perpendiculars from the points (2, 3, 4) and (1, 1, 4) respectively on the plane

3x – 6y + 2z + 11 = 0, then p₁, p₂ are the roots of the equation

• A. p² – 23p 7 = 0
• B. 7p² – 23p + 16 = 0
• C. p² – 17p + 16 = 0
• D. p² – 16p + 7 = 0

Answer 1

Answer: (B)

7p² – 23p + 16 = 0

Answer 2

We have

p₁ $\frac { 3 \times 2 - 6 \times 3 + 2 \times 4 + 11 } { \sqrt { 3 ^ { 2 } + ( - 6 ) ^ { 2 } + ( 2 ) ^ { 2 } } }$= $\frac { 7 } { 7 }$ = 1

and p₂ = = $\frac { 3 \times 2 - 6 \times 1 + 2 \times 4 + 11 } { \sqrt { 3 ^ { 2 } + ( - 6 ) ^ { 2 } + ( 2 ) ^ { 2 } } }$ = $\frac { 16 } { 7 }$

So, that p₁, p₂ are the roots of the equation

p² –$\left( 1 + \frac { 16 } { 7 } \right)$p + $\frac { 16 } { 7 }$ = 0

Ž 7p² – 23p + 16 = 0