Question

Find the angle between the vectors (-9, -8) and (-9,5). Carry your intermediate computations to at least 4 decimalplaces. Round your final answer to the nearest degree.| 。x 6 ?

Answer 1

The vector for (-9,-8) is,

`u=-9\hat{i}-8\hat{j}`

The vector for (-9,5) is,

`v=-9\hat{i}+5\hat{j}`

The formula for the angle between vector u and vector v is,

`\cos \theta=(u\cdot v)/(|u\mleft\Vert v\mright|)`

Determine the angle between vectors.

`\begin{gathered} \cos \theta=\frac{(-9\hat{i}-8\hat{j)}\cdot(-9\hat{i}+5\hat{j})}{\sqrt[]{(-9)^2+(-8)^2}\cdot\sqrt[]{(-9)^2+(5)^2}} \\ =\frac{81-40}{\sqrt[]{145}\cdot\sqrt[]{106}} \\ =\frac{41}{\sqrt[]{15370}} \\ \theta=\cos ^(-1)(0.3307) \\ =70.688 \\ \approx71 \end{gathered}`

So angle between the vector is 71 degree.