Question

Find the magnitude of the scalar multiple, where u = 2, 0 and v = −3, 6.

Answer 1

Based on the given information, the magnitude of the scalar multiple -2v is 13.416

How to find the magnitude of a scalar multiple

To find the magnitude of a scalar multiple, multiply each component of the vector by the scalar, and then calculate the magnitude of the resulting vector.

Given:

u = (2, 0)

v = (-3, 6)

We want to find the magnitude of the scalar multiple -2v.

To obtain -2v, we multiply each component of v by -2:

-2v = (-2 * -3, -2 * 6)

= (6, -12)

Now, we calculate the magnitude of -2v:

||-2v|| =
`\sqrt((6)^2 + (-12)^2)`

=
`\sqrt`(36 + 144)

=
`\sqrt`(180)

= 2 *
`\sqrt`(45)

= 2 *
`\sqrt`(9 * 5)

= 2 * 3 *
`\sqrt`5

= 6 *
`\sqrt`5

= 13. 416

Therefore, the magnitude of the scalar multiple -2v is 13.416

Answer 2

`6√(5)`

Step-by-step explanation:

Given:

u = <2, 0>

v = <-3, 6>

||-2v||

To find:

The magnitude of the scalar multiple

We can go ahead and solve as seen below;

`\begin{gathered} -2v=<-2(-3),-2(6)> \\ \\ -2v=<6,-12> \\ \\ \therefore||-2v||=√(6^2+(-12)^2) \\ \\ =√(36+144) \\ \\ =√(180) \\ \\ =√(36*5) \\ \\ =6√(5) \end{gathered}`