8. Vectors

If vectors $v ⃗=⟨4,3⟩$ and $u ⃗=⟨9,1⟩$, calculate $v ⃗⋅u ⃗$.

If vectors $v⃗=12î$ and $u⃗=100ĵ$, calculate $u ⃗⋅v ⃗$.

If vectors $a⃗=13î$, $⃗b⃗=5î-12ĵ$, and $c⃗=24ĵ$, calculate $b ⃗⋅(a ⃗-c ⃗)$.

If vectors $|a⃗|=3$ and $|b⃗|=7$, and $a⃗\(\cdot\) b⃗=14.85$, determine the angle between vectors $a ⃗$ and $b ⃗$.

In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 3i + j, w = i + 3j

In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 5i - 4j, w = -2i - j

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈2, 1〉, 〈-3, 1〉

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈4, 0〉, 〈2, 2〉