Question

If P be the point (2, 6, 3), then the equation of the plane through P at right angle to OP, O being the origin, is

• A. $2x + 6y + 3z = 7$
• B. $2x - 6y + 3z = 7$
• C. $2x + 6y - 3z = 49$
• D. $2x + 6y + 3z = 49$

Answer 1

Answer: (D)

$2x + 6y + 3z = 49$

Answer 2

Distance of point P from origin $O P = \sqrt { 4 + 36 + 9 } = 7$

Now d.r’s of OP = 2–0, 6 – 0, 3 – 0 = 2, 6, 3

∴ d.c’s of OP = $\frac { 2 } { 7 } , \frac { 6 } { 7 } , \frac { 3 } { 7 }$

∴Equation of plane in normal form is $l x + m y + n z = p$

⇒ $\frac { 2 } { 7 } x + \frac { 6 } { 7 } y + \frac { 3 } { 7 } z = 7$ ⇒ $2 x + 6 y + 3 z = 49$ .