Question

find the angle between <-5,-4> and <-4,-3>

Answer 1

Let a ⃗=-5i-4j
b ⃗=-4i-3j
|a ⃗ |=√((-5)^2+(-4)^2 )=√41
|b ⃗ |=√((-4)^2+(-3)^2 )=5
Let 𝜃 be the angle between the vectors , then
a ⃗.b ⃗=ab cos 𝜃=5 √41 cos 𝜃
Also a ⃗.b ⃗ =(-5i-4j).(-4i-3j)=20+12=32
Hence 32=5√41 cos 𝜃
Cos 𝜃=32/(5√41)
𝜃=cos^(-1)⁡〖32/(5√41)〗