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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 ?A. Alia onlyB. Varun onlyC. both Alia and VarunD. Siddharth only

Answer» Correct Answer - C
`vec(A) = (vec(A))/(|vec(A)|)`
`|vec(A)|` contains number as well as unit. Hence a unit vector has no unit.


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