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,

$a. b=\|a\| .\|b\| \times \cos \theta$

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

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

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

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

$\begin{array}{l}{-10-10=\sqrt{29} \times \sqrt{29} \times \cos \theta} \\\\ {-20=29 \times \cos \theta} \\\\ {\cos \theta=\frac{-20}{29}} \\\\ {\theta=\cos ^{-1} \frac{-20}{29}} \\\\ {\theta=133.60}\end{array}$

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