There are two vectors Force `vec(A) = (hat(i) + 3 hat(j) - hat(k)) N` and Position `vec(B) = (hat(i) + 3 hat(j) - hat(k))m` that can be used by two students Alia and Varun. Following are the steps following by each of them.
Alia : Step 1 : Calculate unit vector of `vec(A)` by dividing it by its magnitude and get
`hat(A) = (hat(i) + 3 hat(j) - hat(k))/(sqrt11)`
Alia : Step 2 : Get a displacement vector of magnitude `10m` using `hat(A)`
Displacement vector `= (10(hat(i) +3 hat(j) - hat(k))/(sqrt11)) m`
Varun : Step 1 : Calculate unit vector of `vec(B)` by dividing `vec(B)` by its magnitude and get,
`hat(B) = ((hat(i) + 3 hat(j) - hat(k))/(sqrt11))`
Varun : Step 2 : Get a force vector of magnitude `10 N` by using `vec(B)`
Force vector `= (10(hat(i) + 3 hat(j) - hat(k)) N)/(sqrt11)`
Siddharth, a third student, comes and says when we divide or multiply a vector by a scalar, then the physical quantity represented by the vector from a displacement vector from a force vector or a force vector from a displacement vector as calculated by Alia and Varun repectivley.
Who is/are correct ?

Options

A. Alia only
B. Varun only
C. both Alia and Varun
D. Siddharth only

Answer

C

Explanation

`vec(A) = (vec(A))/(|vec(A)|)`
`|vec(A)|` contains number as well as unit. Hence a unit vector has no unit.