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

`11.18\ \text{units}`

`10.3^(\circ)`

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

`√((-11)^2+(-2)^2)=5√(5)=11.18`

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

The angle is

`\theta=\tan^(-1)(-2)/(-11)\\\Rightarrow \theta=10.3^(\circ)`

The direction is approximately
`10.3^(\circ)`