If `veca=-hati+hatj+hatk andvecb=2hati+0hatj+hatk` then find vector `vecc` satisfying the following conditions, (i) that it is coplaner with `veca and vecb` , (ii) that it is `bot` to `vecb` and (iii) that `veca.vecc=7`.

Options

A. `-3hati+5hatj+6hatk`
B. `1/2(-3hati+5hatj+6hatk)`
C. `3hati-5hatj+6hatk`
D. `1/2(3hati+5hatj-6hatk)`

Answer

B

Explanation

Since `vecX` is in the plane of `veca` and `vecb` and is perpendicular to `vecb`.
`:.vecX=lamda{vecbxx(vecaxxvecb)}`
`impliesvecX=lamda[(vecb.vecb)veca-(vecb.veca)vecb]`
`implies vecX=lamda[5(-hati+hatj+hatk)-(-1)(2hati+0hatj+hatk)]`
`impliesvecX=lamda[-5hati+5hatj+5hatk+2hati+0hatj+hatk]`
`impliesvecX=lamda[3hati+5hatj+6hatk]`
Now,
`veca.vecX=7`
`implies(-hati+hatj+hatk).lamda(-3hati+5hatj+6hatk)=7`
`implieslamda(3+5+6)=7implieslamda=1/2`
Hence `vecX=1/2(-3hati+5hatj+6hatk)`