If a vector `(2hati+3hatj+8hatk)` is perpendicular to the vector `(4hatj-4hati+alpha hatk)`, then the value of `alpha` is :

Options

A. -1
B. 1
C. `-(1)/(2)`
D. `(1)/(2)`

Answer

C

Explanation

`vec P =2hati + 3hatj +8hatk and vec Q= 4hatj -4hati + alpha k=-4hati +4hatj+alpha k`
If `vec P bot vec Q" then "vec P cdot vec Q=0`
`therefore (2hati +3hatj+8hatk) cdot (-4hati+4hatj+alpha k)=0`
`therefore [(2xx(-4)]hati cdot hati+(3xx4) hatj cdot hatj+(8 xx alpha) hatk cdot hatk=0`
`therefore -8 +12 +8 alpha =0`
`therefore 8 alpha =-4" "therefore alpha =-(1)/(2)`