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In the following cases, determine whethe...

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them :
(a) 7x + 5y + 6z + 30 = 0 and 3x - y-10z + 4 = 0
(b) 2x + y + 32 - 2 = 0 and x - 2y + 5 = 0
(c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z-1 = 0
(d) 2x – y + 3z-1 = 0 and 2x - y + 3z + 3 = 0
(e) 4x + 8y + z - 8 = 0 and y + z - 4 = 0

Text Solution

Verified by Experts

The correct Answer is:
(a) `therefore theta=cos^(-1)(2/5)`
(b) `=0`
(c) `=2/3`
`therefore` Normal of the planes are parallel
`therefore` Given planes are parallel
(d) `therefore` Normal of the planes are parallel
`therefore` Given planes are parallel
(e) `therefore theta=45^@`
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