Vectors $$\overrightarrow { \mathrm { A } }$$ and $$\vec { B }$$ have equal magnitudes.Which statement is always true?
A) $$\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = 0$$ .
B) $$\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = 0$$ .
C) $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } }$ is perpendicular to $\overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } }$ .
D) $\overrightarrow { \mathrm { B } } - \overrightarrow { \mathrm { A } }$ is perpendicular to $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } }$ .
E)The magnitude of $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } }$ equals the magnitude of $\overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } }$ .

Question

Quizplus · Accepted Answer

The only statement that is always true when two vectors have equal magnitudes is that their dot product is equal to zero, meaning they are perpendicular. Therefore, choice C is the correct answer. The other choices may or may not be true depending on the specific vectors being considered.

Vectors A→\overrightarrow { \mathrm { A } }A And B⃗\vec { B }B

Vectors $\overrightarrow { \mathrm { A } }$ And $\vec { B }$