Answer: To find the magnitude and direction of vector RS, we first need to find the components of the vector, which are given by the differences in the x- and y-coordinates of R and S:
v = RS = <(-14) - (-2), 8 - 11> = <-12, -3>
The magnitude of v is given by the formula ||v|| = sqrt(a^2 + b^2), where a and b are the x- and y-components of v:
||v|| = sqrt((-12)^2 + (-3)^2) = sqrt(144 + 9) = sqrt(153) = 12.37
The direction of v is given by the angle that it makes with the positive x-axis, measured counterclockwise. We can find this angle using the formula theta = arctan(b/a), where a and b are the x- and y-components of v:
theta = arctan(-3/-12) = arctan(0.25) = -14.04 degrees (rounded to the nearest hundredth)
Therefore, the magnitude of RS is 12.37, and the direction of RS is 14.04 degrees below the negative x-axis.
Explanation: