Question

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

U= (4,-8) V= (-6, -3)

Answer 1

90°

Explanation:

Given the vectors:

`\displaystyle{\vec v = \langle -6, -3\rangle \ \: \text{and} \ \: \vec u = \langle 4, -8 \rangle}`

You can find the angle between two vectors by solving for θ in the equation:

`\displaystyle \cos \theta`

Where:

`\displaystyle{\vec v * \vec u = v_xu_x + v_yu_y}\\\\\displaystyle\\\\\displaystyle`

Therefore:

`\displaystyle\vec v \\\\\displaystyle{(-6)(4)+(-3)(-8) = √((-6)^2+(-3)^2) \cdot √(4^2+(-8)^2) \cos \theta}\\\\\displaystyle{-24+24=√(36+9)\cdot √(16+64)\cos \theta}\\\\\displaystyle{0=√(45)\cdot √(80)\cos \theta}\\\\\displaystyle{(0)/(√(45)\cdot √(80))=\cos \theta}\\\\\displaystyle{0=\cos \theta}\\\\\displaystyle{\theta = 90^(\circ)}`

Therefore, the angle between two vectors is 90 degrees.