Answer: Hence, the angle between the given vectors is 1.8°.
Step-by-step explanation:
Since we have given that
[tex]\vec{u}=-5\hat{i}-4\hat{j}\\\vec{v}=-4\hat{i}-3\hat{j}[/tex]
We need to find the angle between the given vectors:
[tex]\cos\theta=\dfrac{\vec{u}.\vec{v}}{\mid\vec{u}\mid.\mid \vec{v}\mid}\\\\\cos \theta=\dfrac{(-5\hat{i}-4\hat{j}).-4\hat{i}-3\hat{j}}{\sqrt{(-5)^2+(-4)^2}\sqrt{(-4)^2+(-3)^2}}\\\\\cos \theta=\dfrac{20+12}{\sqrt{41}\sqrt{25}}\\\\\cos \theta=\dfrac{32}{5\sqrt{41}}\\\\\theta=\cos^{-1}(0.99)\\\\\theta=1.78^\circ[/tex]
Hence, the angle between the given vectors is 1.8°.
