8. Vectors

True or false: If $a ⃗=⟨3,-2⟩$ and $b ⃗$ has initial point $(-10,5)$ & terminal point $(-7,3)$, then $a ⃗=b ⃗$.

True or false: If $a ⃗=⟨3,2⟩$ and $b ⃗$ has initial point $(3,-1)$ & terminal point $(6,1)$, then $a ⃗=b ⃗$.

Let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (2, -5), P₂ = (-6, 6)

If vector $v ⃗=⟨-4,-10⟩$, calculate the magnitude $|v ⃗ |$.

If vectors $v ⃗=⟨4,1⟩$, $u ⃗=⟨-8,3⟩$, and $w ⃗=⟨-2,-1⟩$, calculate $w ⃗-3(v ⃗+u ⃗)$.

If vectors $v ⃗=⟨2,1⟩$, $u ⃗=⟨3,4⟩$, and $w ⃗=⟨-1,1⟩$, calculate $v ⃗+u ⃗-w ⃗$.

Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.

||v|| = 8, θ = 45°

Let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j.

P₁ = (-1, 6), P₂ = (7, -5)

Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.

||v|| = 10, θ = 330°

If vector $v ⃗$ has initial point $(-1,2)$ and terminal point $(9,5)$, calculate the magnitude $|v ⃗ |$.