Question

Find the angle between the vectors u=i-9j and v=8i+5j

Answer 1

Answer:
`\cos^(-1) \left((-37)/(√(7298)) \right) \approx 115.665^(\circ)`

Explanation:

`u \cdot v=(1)(8)+(-9)(5)=-37\\\\|u|=\sqrt{1^(2)+(-9)^(2)}=√(82)\\\\|v|=\sqrt{8^(2)+5^(2)}=√(89)\\\\\cos \theta=(-37)/(√(82)√(89))\\\\\theta=\cos^(-1) \left((-37)/(√(82)√(89)) \right)\\\\\theta=\boxed{\cos^(-1) \left((-37)/(√(7298)) \right) \approx 115.665^(\circ)}`