Question

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

• A. $\vec{A}+\vec{B}$
• B. $A_x+B_y$
• C. $\left|\vec{A}+\vec{B}\right|$
• D. Angle between $\vec{A}$ and $\vec{B}$

Answer 1

Answer: (B)

A vector, its magnitude and the angle between two vectors do not depend on the choice of the orientation of the coordinate axes. So $\vec{A}+\vec{B}$, $\left|\vec{A}+\vec{B}\right|$, 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.