Question

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

• A. $\overleftarrow{A} + \overrightarrow{B}$
• B. $A_{x} + B_{y}$
• C. $|\overleftarrow{A} + \overrightarrow{B}|$
• D. Angle between $\overrightarrow{A}$and $\overrightarrow{B}$

Answer 1

Answer: (B)

$A_{x} + B_{y}$

Answer 2

A vector, its magnitude and the angle between two vector do not depend on the choice of the orientation of the coordinate axes. So $\overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } | \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } |$ $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$are independent of the orientations of coordinate axes.

But the quantity $A_{x} + B_{y}$depends upto the

magnitude of the components along x and y – axes, so it will changes with changes in coordinate axes.