Question

The equation of the plane passing through (1, 1, 1) and

(1, –1, –1) and perpendicular to $2x - y + z + 5 = 0$is

• A. $2x + 5y + z - 8 = 0$
• B. $x + y - z - 1 = 0$
• C. $2x + 5y + z + 4 = 0$
• D. $x - y + z - 1 = 0$

Answer 1

Answer: (B)

$x + y - z - 1 = 0$

Answer 2

Any plane passing through (1, 1, 1) is $a ( x - 1 ) + b ( y - 1 ) + c ( z - 1 ) = 0$ .....(i)

Plane (i) is also passing through (1, –1, –1)

or, $0 . a - 2 b - 2 c = 0$ or $0 . a - b - c = 0$

or, $0 . a + b + c = 0$ ......(ii)

Plane (i) is perpendicular to $2 x - y + z + 5 = 0$

So, $2 a - b + c = 0$ .....(iii)

From (ii) and (iii), $a = b = 1 , c = - 1$

Substituting in (i) we have $x + y - z - 1 = 0$