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Find the angle between the planes 2x+y+z...

Find the angle between the planes `2x+y+z-1=0 and 3x+y+2z-2=0`,

A

`1/sqrt(2)` units

B

`sqrt(2)` units

C

`3/sqrt(2)` units

D

`sqrt(3)/2` units

Text Solution

Verified by Experts

The correct Answer is:
A
Any plane passing through first line is `2x+y=z-1+lambda(3x+y+2z-2)=0`
Line x=y=z is passing through the point O(0,0,).
Required shortest distance = distance of O from the member plane of above family which is parallel to the line x=y=z
If plane is parallel to the line,
`(2x+3lambda)1+(1+lambda)1+(1+2lambda)1=0`
`rArr lambda=-2/3`
Equation of plane is
`3(2x+y+z-1)-2(3x+y+2z-2)=0`
or `y-z+1=0`
Its distance from (0,0,0) is `1/sqrt(2)`.
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