8. Vectors

In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = -6i - 5j, w = -10i - 8j

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 $b ⃗$.

If vectors $a⃗=4î$ and $b⃗=3î-2ĵ$, determine the angle between vectors $a ⃗$ and $b ⃗$.

If vectors $|v ⃗ |=12$, $|u ⃗ |=100$ and the angle between $v ⃗$ & $u ⃗$ is $\(\theta\)=\(\frac{\pi}{6}\)$, calculate $v ⃗⋅u ⃗$ .

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

In Exercises 5–8, let v = -5i + 2j and w = 2i - 4j Find the specified vector, scalar, or angle. v ⋅ w

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

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

〈1, 6〉, 〈-1, 7〉

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

3i + 4j, j