Question

I need help with this practice I believe the subject for this is complex numbers and vectors I will send you an additional picture that goes along with this, it is a graph, use the graph to answer

Answer 1

- In order to plot these vectors using Parallelogram law, we need to write them in rectangular form i.e. in terms of the x and y-components.

- This is done below:

`\begin{gathered} \vec{a}=-3i-5j \\ \vec{b}=i+4j \end{gathered}`

- We can then proceed to plot the vectors on a graph.

- For vector a, the line of magnitude extends from the origin (0, 0) to the point (-3, -5) while the line of the magnitude of vector b extends from the origin (0, 0) to the point (1, 4).

- This is shown below:

- The vector addition of both vectors is given below:

`\begin{gathered} \vec{a}+\vec{b}=-3i-5j+(i+4j) \\ \text{ Add only magnitudes of the same component} \\ \vec{a}+\vec{b}=-3i+i-5j+4j \\ \\ \therefore\vec{a}+\vec{b}=-2i-j \end{gathered}`

- This implies that the vector addition of both vectors extends from the origin (0,0) to the point (-2, -1)

- This is depicted below: