1.

Let P denotes the plane consisting of all points that are equidistant from the points A(-4,2,1) and B(2,-4,3) and Q be the plane, x-y+cz=1 where c in R. If the angle between the planes P and Q is 45^(@) then the product of all possible values of c is

Answer»

`-17`
`-2`
17
`24//27`

SOLUTION :`vecn_(1) = 3hati-3hatj+hatk` and `vecn_(2) = hati-hatj+chatk`
`COS 45^(@) = |(vecn_(1).vecn_(2))/(|vecn_(1)||vecn_(2)|)|=|((3+3+c)/(sqrt(19)sqrt(2+c^(2))))|`
`THEREFORE 2(6+c)^(2) = 19(2+c^(2))`
`rArr 2(36+c^(2)+12c)=38+19c^(2)`
`rArr 17c^(2)-24c-34=0`


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