Vectors ` vec a=-4 hat i+3 hat k ; vec b=14 hat i+2 hat j-5 hat k` are laid off from one point. Vector ` hat d` , which is being laid of from the same point dividing the angle between vectors ` vec aa n d vec b` in equal halves and having the magnitude `sqrt(6),` is a. ` hat i+ hat j+2 hat k` b. ` hat i- hat j+2 hat k` c. ` hat i+ hat j-2 hat k` d. `2 hat i- hat j-2 hat k`

Options

A. `hati+hatj + 2hatk`
B. `hati-hatj+2hatk`
C. `hati+hatj-2hatk`
D. `2hati-hatj-2hatk`

Answer

A

Explanation

`hat a = (-4i + 3hatk)/(5) , hatb = (14hati + 2hatj - 5hatk)/(15) `
A vector `vecV` bisecting the angle between `veca and vecb` is
`" "vecV = hata + hat b `
`" "= (-12hati + 9hatk + 14hati + 2hatj -5hatk)/(15)`
`" " = (2hati + 2hatj + 4hatk)/(15)`
Required vector `vecd = sqrt6 hat V = hat i + hatj + 2hatk`