Question

If the distance of the point (1, 1,1) from the origin is half its distance from the plane $x + y + z + k = 0$, then $k =$

• A. $\pm 3$
• B. $\pm 6$
• C. –3, 9
• D. $3, - 9$ (e) 3, 9

Answer 1

Answer: (D)

$3, - 9$ (e) 3, 9

Answer 2

Distance of the point (1,1,1) from origin $= \sqrt { ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } } = \sqrt { 3 }$

Distance of the point (1,1,1) from $x + y + z + k = 0$ is, $\pm \frac { ( 1 ) + ( 1 ) + ( 1 ) + k } { \sqrt { ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } + ( 1 ) ^ { 2 } } } = \pm \frac { k + 3 } { \sqrt { 3 } }$

According to question, $\sqrt { 3 } = \pm \frac { 1 } { 2 } \left( \frac { k + 3 } { \sqrt { 3 } } \right)$

⇒ $6 = \pm ( k + 3 )$ ⇒ $k = 3 , - 9$ .