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Two vectors are given by vec(A)= hat(i) ...

Two vectors are given by `vec(A)= hat(i) + 2hat(j) + 2 hat(k) and vec(B)= 3 hat(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 )`?

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))`

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