Question

2.Let u = (2,5) and v be a vector with a magnitude of 5 at an angle of 143.130.

Represent the following vectors geometrically on a coordinate plane and
symbolically using magnitude, direction, and components:
u, v, u + v, 2u, and - 3v.

Answer 1

See below

Explanation:

Recall that
`\overrightarrow{v}=\langle ||\overrightarrow{v}||cos\theta,||\overrightarrow{v}||sin\theta\rangle` for a vector
`\overrightarrow{v}` with magnitude
`||v||` that makes an angle
`\theta` with the positive x-axis.

Thus, the component form of vector
`\overrightarrow{v}` is
`\overrightarrow{v}=\langle5cos(143.13^\circ),5sin(143.13^\circ)\rangle=\langle-4,3\rangle`

Therefore:

`u=\langle2,5\rangle`

`v=\langle-4,3\rangle`

`u+v=\langle2,5\rangle+\langle-4,3\rangle=\langle2+(-4),5+3\rangle=\langle-2,8\rangle`

`2u=2\langle2,5\rangle=\langle2(2),2(5)\rangle=\langle4,10\rangle`

`-3v=-3\langle-4,3\rangle=\langle-3(-4),-3(3)\rangle=\langle12,-9\rangle`

View the attached graph to see each vector graphed

Answer 2

I Hope This Help

Explanation: