The equation of plane passing through (1,2,-1) and containing the… - Vidyadip

MCQ

The equation of plane passing through $(1,2,-1)$ and containing the lines whose direction ratios are $2,1,3$ and $4,1,2$

✓
$x-5 y+z+10=0$
B
$x-5 y-z+10=0$
C
$x+5 y+z+10=0$
D
$x+5 y-z-10=0$

✓

Answer

Correct option: A.

$x-5 y+z+10=0$

(A)
Let $\left(x_1, y_1, z _1\right)=(1,2,-1)$,
$a_1, b_1, c_1=2,1,3$ and $a_2, b_2, c_2=4,1,2$
$\therefore \quad$ the equation of required plane is $\left|\begin{array}{ccc}x-1 & y-2 & z+1 \\ 2 & 1 & 3 \\ 4 & 1 & 1\end{array}\right|=0$
$\Rightarrow(x-1)(-2)+(y-2)(10)+(z+1)(-2)=0$
$\Rightarrow-2 x+2+10 y-20-2 z-2=0$
$\Rightarrow x-5 y+z+10=0$

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