If a vector `2hat(i)+3hat(j)+8hat(k)` is perpendicular to the vector `4hat(j)-4hat(i)+alpha hat(k)`. Then the value of `alpha` is

Options

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

Answer

C

Explanation

Given Vectors can be rewritten as `vec(A)= 2hat(i)+3hat(j)+8hat(k)` and `vec(B)= -4hat(i)+4hat(j)+alpha hat(k)`
Dot product of these Vectors should be equal to Zero because they are perpendicular
`:. vec(A).vec(B)= -8+12+8alpha= 0implies 8 alpha= -4implies alpha= -1//2`