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Find x such that the four points A\ (3,...

Find x such that the four points `A\ (3,\ 2,\ 1)`, `B(4, x ,\ 5)`, `C\ (4,\ 2,\ 2)`and `D\ (6,\ 5,\ 1)`are coplanar

Text Solution

Verified by Experts

Here,
`vec(AB) = hati+(x-2)hatj+4hatk`
`vec(AC) = hati+0hatj-3hatk`
`vec(AD) = 3hati+3hatj-2hatk`
Now, the given four points are coplanar if `vec(AB), vec(AC) and vec(AD)` are coplanar.
It means, their determinant is `0`.
`|[1,x-2,4],[1,0,-3],[3,3,-2]|= 0`
Now,`C_3->3C_1+C_3`
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