Question

Equation of a plane bisecting the angle between the planes 2x – y + 2z + 3 = 0 and 3x –2y + 6z + 8 = 0 is -`

• A. 5x – y – 4z – 45 = 0
• B. 5x – y – 4z – 3 = 0
• C. 23x + 13y + 32z – 45 = 0
• D. 23x – 13y + 32z + 5 = 0

Answer 1

Answer: (B)

5x – y – 4z – 3 = 0

Answer 2

Equations of the planes bisecting the angle between the given planes are

$\frac{2x - y + 2z + 3}{\sqrt{2^{2} + ( - 1)^{2} + 2^{2}}}$

= ±$\frac{3x - 2y + 6z + 8}{\sqrt{3^{2} + ( - 2)^{2} + 6^{2}}}$

Ž 7(2x – y + 2z + 3) = ± 3(3x – 2y + 6z + 8)

Ž 5x – y –4z – 3 = 0 taking the +ve sign, and

23x – 13y + 32z + 45 = 0

taking the –ve sign.