Question

If u3i + 7j and v=8i + 1j, find the angle between them.

Answer 1

STEP 1

Establish the problem.

We need to find the angles the vectors given make with the horizontal.

The vectors are given in unit vector form and will require diagrammatic representation as well.

u = 3i + 7j means vector u goes 3 units along the x asis and 7 units along the y axis

v = 8i + j means vector u goes 8 units along the x asis and 1 units along the y axis

We now get the plot.

STEP 2:

Get angles that the two vectors make with the horizontal and subtract to get answer.

Angle u to the horixontal is given as:

`\begin{gathered} \text{Tan }\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \\ \text{Tan u}=(7)/(3) \\ u=tan^(-1)((7)/(3))=66.8\text{ degrees} \end{gathered}`

Angle v to the horixontal is given as:

`\begin{gathered} \text{Tan }\theta=\frac{y\text{ coordinate}}{x\text{ coordinate}} \\ \text{Tan u}=(1)/(8) \\ u=tan^(-1)((7)/(3))=7.1\text{ degrees} \end{gathered}`
`\text{Therefore, the angle between the two is given as }\theta=\text{ 66.8 - 7.1 = 59.7 degrees}`