Q34 / 90 · JEE Main 2019 (12 Apr Shift 2) · Mathematics

A plane which bisects the angle between the two given planes $2 x - y + 2 z - 4 = 0$ and $x + 2 y + 2 z - 2 = 0$ , passes through the point

A
$(2, 4, 1)$
B
$(1, - 4, 1)$
C
$(1, 4, - 1)$
Correct answer
D
$(2, - 4, 1)$

Solution

Equation of bisector of angle

\frac{2 x - y + 2 z - 4}{3} = \pm \frac{x + 2 y + 2 z - 2}{3}

(+)

gives

x - 3 y = 2

(-)

gives

3 x + y + 4 z = 6

therefore

(2, - 4, 1)

satisfies the above equation.

Hence, the correct answer is option: 'D'.

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