A plane passing through (−1, 2, 3) and whose normal makes equal a… - Vidyadip

MCQ

A plane passing through $(−1, 2, 3)$ and whose normal makes equal angle with the coordinate axes is:

A
$x + y + z + 4 = 0$
B
$x − y + z + 4 = 0$
✓
$x + y + z − 4 = 0$
D
$x + y + z = 0$

✓

Answer

Correct option: C.

$x + y + z − 4 = 0$

Since normal makes equal angles with coordinate axis.
So, it intercept with all the axis will be same.
So equation of plane will be
$\frac{\text{x}}{\text{a}}+\frac{\text{y}}{\text{a}}+\frac{\text{x}}{\text{a}}=1$
$\Rightarrow x + y + z = a$
Now, it passes through $(−1, 2, 3),$ so
$−1 + 2 + 3 = a$
$\Rightarrow a = 4$
$\Rightarrow x + y + z − 4 = 0$

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