Q8 of 181 Page 1217

Find the value of λ for which the planes x – 4y + λz + 3 = 0 and 2x + 2y + 3z = 5 are perpendicular to each other.

To find an angle in Cartesian form, for the standard equation of planes

For θ=90°, cos90°=0

On comparing with the standard equation of the plane,

2 + (-8) + 3λ=0

-6 + 3λ=0

λ=2

Prove that the plane 2x + 2y + 4z = 9 is perpendicular to each of the planes x + 2y + 2z – 7 = 0 and 5x + 6y + 7z = 23.

Show that the planes 2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z - 1 = 0 are parallel.

Write the equation of the plane passing through the origin and parallel to the plane 5x - 3y + 7z + 11 = 0.

Find the equation of the plane passing through the point (a, b, c) and parallel to the plane