Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <-5, -4>, v = <-4, -3>

Answer 1

Answer: Hence, the angle between the given vectors is 1.8°.

Explanation:

Since we have given that

`\vec{u}=-5\hat{i}-4\hat{j}\\\vec{v}=-4\hat{i}-3\hat{j}`

We need to find the angle between the given vectors:

`\cos\theta=\frac{\vec{u}.\vec{v}}{\mid\vec{u}\mid.\mid \vec{v}\mid}\\\\\cos \theta=\frac{(-5\hat{i}-4\hat{j}).-4\hat{i}-3\hat{j}}{√((-5)^2+(-4)^2)√((-4)^2+(-3)^2)}\\\\\cos \theta=(20+12)/(√(41)√(25))\\\\\cos \theta=(32)/(5√(41))\\\\\theta=\cos^(-1)(0.99)\\\\\theta=1.78^\circ`

Hence, the angle between the given vectors is 1.8°.

Answer 2

The question ask to find the angle between the given vector to the nearest tenth of a degree and base on the value or the coordinates of each vector, the possible value of the angle base on the said vectors is 1.8 degree. I hope you are satisfied with my answer and feel free to ask for more