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If the three vectors are coplanar, then ...

If the three vectors are coplanar, then find `x`.
`A=hati-2hatj+3hatk, B=xhatj+3hatk, C=7hati+3hatj-11hatk`

A

`36//21`

B

`-51//32`

C

`51//32`

D

`-36//21`

Text Solution

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(b) The three vectors are coplanar, if their scalar tripler product is zero.
i.e. `A.(BxxC)=0=|(1, -2, 3),(0, x, 3),(7, 3, -11)|=0`
`(1)[-x(11)-9=+2(0-21)+3(0-7x)=0`
`-11x-9-42-21x=0implies-32x-51=0impliesx=- 51/32`
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