Two vectors are given by `vec(A) = hat(i) + 2hat(j) + 2hat(k)` and `vec(B) = 3hat(i) + 6hat(j) + 2hat(k)`. Another vector `vec(C )` has the same magnitude as `vec(B)` but has the same direction as `vec(A)`. Then which of the following vectors represents `vec(C )` ?

Options

A. `(7)/(3) (hat(i) + 2hat(j) + 2hat(k))`
B. `(3)/(7) (hat(i)- 2hat(j) + 2hat(k))`
C. `(7)/(9) (hat(i)- 2hat(j)+ 2hat(k))`
D. `(9)/(7) (hat(i) + 2hat(j) + 2hat(k))`

Answer

A

Explanation

Vector `vec(C) = (vec(A))/(A) xx |vec(B)|`
`= (hat(i) + 2hat(j) + 2hat(k))/(sqrt((1)^(2)+ (2)^(2) + (2)^(2))) xx sqrt(3^(2) + (6)^(2) + (2)^(2))`
`= (7)/(3) (hat(i) + 2hat(j) + 2hat(k))`