Question

Vector z = <5, -3> is subtracted from vector w = <-6, -5>. The magnitude of the resulting vector is approximately ______-, and its angle of direction is approximately ________-°.

Answer 1

Answer:

$11.18\ \text{units}$

$10.3^{\circ}$

Step-by-step explanation:

$w=<-6,-5>$

$z=<5,-3>$

z is subtracted from w so

$w-z=<-6-5,-5-(-3)>\\\Rightarrow w-z=<-11,-2>$

Magnitude is given by

$\sqrt{(-11)^2+(-2)^2}=5\sqrt{5}=11.18$

The magnitude of the resulting vector is approximately $11.18\ \text{units}$.

The angle is

$\theta=\tan^{-1}\dfrac{-2}{-11}\\\Rightarrow \theta=10.3^{\circ}$

The direction is approximately $10.3^{\circ}$