Question

Which of the following is independent of the choice of the coordinate system?

• A. $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}}$
• B. $\left({\mathrm{P}}_{\mathrm{x}}+{\mathrm{Q}}_{\mathrm{x}}+{\mathrm{R}}_{\mathrm{x}}\right)$
• C. ${\mathrm{P}}_{\mathrm{x}}\hat{\mathrm{i}}+{\mathrm{Q}}_{\mathrm{x}}\hat{\mathrm{j}}+{\mathrm{R}}_{\mathrm{z}}\hat{\mathrm{k}}$
• D. None of these

Answer 1

The correct option is A

$\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}}$

Explanation for correct options

Option A:

1. $\overrightarrow{\mathrm{P}}+\overrightarrow{\mathrm{Q}}+\overrightarrow{\mathrm{R}}$ in this we can plot any vector on any coordinate.
2. There is no pre condition that vector P should be on a definite coordinate.
3. Free vector states to a vector which is neither a line nor a point and something that can move around the space freely though free vector has a fixed direction and fixed magnitude.

Explanation for incorrect options

Option B&C:

1. $\left({\mathrm{P}}_{\mathrm{x}}+{\mathrm{Q}}_{\mathrm{x}}+{\mathrm{R}}_{\mathrm{x}}\right)$ in this coordinate are predefined.

Hence, the correct answer is option (A).