Question

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`

Answer 1

(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`