Question

(b) Find the angle between u and v to the nearest degree.

Answer 1

Question 1 (b)

`u \cdot v=11\\\\|u|=\sqrt{3^(2)+(-1)^(2)}=√(10)\\\\|v|=\sqrt{4^(2)+1^(2)}=√(17)`

So,

`\cos \theta=(11)/(√(10)√(17))\\\\\theta=\cos^(-1) \left((11)/(√(10)√(17)) \right) \approx \boxed{32^(\circ)}`

Question 2 (b)

`u \cdot v=22\\\\|u|=\sqrt{5^(2)+2^(2)}=√(29)\\\\|v|=\sqrt{4^(2)+1^(2)}=√(17)`

So,

`\cos \theta=(22)/(√(29)√(17))\\\\\theta=\cos^(-1) \left((22)/(√(29)√(17)) \right) \approx \boxed{8^(\circ)}`