Find the equation of the plane parallel to plane 2x 3y + 6z 5 = 0 - Maths - Matrices

Question

Find the equation of the plane parallel to plane 2x
− 3y + 6z − 5 = 0 at a distance of 4
units from it

Santosh Kumar · Accepted Answer

The equation of the plane parallel to the plane 2x – 3y + 6z – 5 = 0 is given by, 2x – 3y + 6z + d = 0.

Now, distance between two parallel planes ax + by + cz + d₁ = 0 and ax + by + cz + d₂ = 0 is given by,

$\frac{| d_{1} - d_{2} |}{\sqrt{a^{2} + b^{2} + c^{2}}}$

So, distance between 2x – 3y + 6z – 5 = 0 and 2x – 3y + 6z + d = 0, distance, D

$= \frac{| - 5 - d |}{\sqrt{(2)^{2} + (- 3)^{2} + (6)^{2}}}$

$\Rightarrow 4 = \frac{| - (5 + d) |}{\sqrt{4 + 9 + 36}} \Rightarrow \frac{| - (5 + d) |}{\sqrt{49}} = 4 \Rightarrow \frac{(5 + d)}{(7)} = 4 \Rightarrow 5 + d = 28 \Rightarrow d = 28 - 5 \Rightarrow d = 23$

So, equation of the required plane, 2x – 3y + 6z + 23 = 0

2

Find the equation of the plane parallel to plane 2x − 3y + 6z − 5 = 0 at a distance of 4 units from it