If `vec A =2 hat i+ 3 hat j+ 8 hat k` is perpendicular to `vec B= 4 hat j -4 hat i+ alpha hat k` , then the value of `alpha`

Options

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

Answer

B

Explanation

Given :
`A=2hat(i)+3hat(j)+8hat(k)`
`B=4hat(j)-4hat(i)+alpha hat(k)`
`=-4hat(i)+4hat(j)+alpha hat(k)`
`A _|_ B` Hence, A. B = 0
`rArr (2hat(i)+3hat(j)+8hat(k))(-4hat(i)+4hat(j)+alpha hat(k))=0`
`rArr -8+12+8alpha=0`
`rArr 8alpha + 4=0`
`rArr 8alpha =-4`
`alpha =-(4)/(8)=-(1)/(2)`