First slide

Vectors

Question

Which of the following quantities is dependent of the choice of orientation of the coordinate axes?

Moderate

A

$\vec{A} + \vec{B}$
B

$A_{x} + B_{y}$
C

$| \vec{A} + \vec{B} |$
D

Angle between A and B

Solution

A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes. So $\vec{A} + \vec{B}, | \vec{A} + \vec{B} |$ angle between $\vec{A} and \vec{B}$ are independent of the orientation of the coordinate axes.
But the quantity $A_{x} + B_{y}$ depends upon the magnitude of the components along x and y-axes, so it will change with change in coordinate axes.

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