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 $b ⃗$.

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 = -6i - 5j, w = -10i - 8j

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

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

2i + 2j, -5i - 5j

Determine whether each pair of vectors is orthogonal.

〈1, 1〉, 〈1, -1〉

Determine whether each pair of vectors is orthogonal.

√5i - 2j, -5i + 2 √5j

Determine whether each pair of vectors is orthogonal.

i + 3√2j, 6i - √2j