1. Tardigrade
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  4. Which of the following quantities is dependent of the choice of orientation of the coordinate axes?

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

Motion in a Plane

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 $\vec{A}+\vec{B}$, $\left|\vec{A}+\vec{B}\right|$, 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.