Question

Find the angle between u = (-2,-5) and v = (5,2)

Answer 1

The angle between u = (-2,-5) and v = (5,2) is 134 degrees approximately.

Solution:

Given, two vectors are u = (-2, -5) and v = (5, 2)

We have to find the angle between two vectors.

We know that,

`a. b=\|a\| .\|b\| * \cos \theta`

where
`\theta` is angle between vectors a and b

`\text { Now vectors are }(-2 \vec{\imath}-5 \vec{\jmath}) \text { and }(5 \vec{\imath}+2 \vec{\jmath})`

`(-2 \vec{\imath}-5 \vec{\jmath}) \cdot(5 \vec{\imath}+2 \vec{\jmath})=\sqrt{(-2)^(2)+(-5)^(2)} * \sqrt{5^(2)+2^(2)} * \cos \theta`

`\text { since }\|a\|=\sqrt{x^(2)+y^(2)} \text { for } a=x \vec{\imath}+y \vec{\jmath}`

`\begin{array}{l}{-10-10=√(29) * √(29) * \cos \theta} \\\\ {-20=29 * \cos \theta} \\\\ {\cos \theta=(-20)/(29)} \\\\ {\theta=\cos ^(-1) (-20)/(29)} \\\\ {\theta=133.60}\end{array}`

Hence, the angle between given two vectors is 134 degrees approximately.