Question

The equation of a plane containing the line $\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$ and the point (0,7, - 7) is

• A. $x+y + z = 0$
• B. $x+ 2y + z=21$
• C. $3x-2y + 5z+35 = 0$
• D. $3x + 2y + 5z+21 = 0$

Answer 1

Answer: (A)

$x+y + z = 0$

Answer 2

The equation of a plane containing the line $\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$ is a $(x + 1) + b (y - 3) + c (z + 2) = 0$ where $- 3a + 2b + c = 0 \quad\quad...\left(A\right)$ This passes through $\left(0, 7, - 7\right)$ $\therefore a \left(0 + 1\right) + b \left(7 - 3\right) + c \left(- 7 + 2\right) = 0$ $\Rightarrow a + 4b - 5c = 0 \quad\quad...\left(B\right)$ On solving equation $\left(A\right)$ and $\left(B\right)$ we get $a=1, b=1, c=1$ $\therefore$ Required plane is $x + 1 + y - 3 + z + 2 = 0$ $\Rightarrow x+y + z= 0$