The components of vectors $\overrightarrow { \mathrm { A } }$ and $\overrightarrow { \mathrm { B } }$ are given as follows: A_x = 7.6 B_x = -5.1
A_y = -9.2 B_y = -6.8
What is the magnitude of the vector difference $\overrightarrow { \mathrm { B } }$ - $\overrightarrow { \mathrm { A } }$ ?

Question

The components of vectors

\overrightarrow { \mathrm { A } }

and

\overrightarrow { \mathrm { B } }

are given as follows: A_x = 7.6 B_x = -5.1
A_y = -9.2 B_y = -6.8
What is the magnitude of the vector difference

\overrightarrow { \mathrm { B } }

-

\overrightarrow { \mathrm { A } }

?

Quizplus · Accepted Answer

The magnitude of the vector difference $\overrightarrow { \mathrm { B } }$ - $\overrightarrow { \mathrm { A } }$ is given by:$$|\overrightarrow { \mathrm { B } }\) - $\overrightarrow { \mathrm { A } }$| = \sqrt{(B_x - A_x)^2 + (B_y - A_y)^2}$$$$= \sqrt{(-5.1 - 7.6)^2 + (-6.8 - (-9.2))^2}$$$$= \sqrt{(-12.7)^2 + (2.4)^2}$$$$= \sqrt{161.29 + 5.76}$$$$= \sqrt{167.05}$$$$= 12.92$$Therefore, the magnitude of the vector difference $\overrightarrow { \mathrm { B } }$ - $\overrightarrow { \mathrm { A } }$ is 12.92, which is closest to choice A) 13.

The Components of Vectors A→\overrightarrow { \mathrm { A } }A

The Components of Vectors $\overrightarrow { \mathrm { A } }$