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

Question

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

x + y + z + 4 = 0
x − y + z + 4 = 0
x + y + z − 4 = 0
x + y + z = 0

✓

Answer

x + y + z − 4 = 0

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

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