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

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