8. Vectors

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $u ⃗+v ⃗$

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $u ⃗-v ⃗$.

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $\(\frac\)12u⃗+v⃗$.

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $-2u ⃗+3v ⃗$.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||u||.

In Exercises 1–4, u and v have the same direction. In each exercise: Is u = v? Explain.

In Exercises 1–4, u and v have the same direction. In each exercise: Find ||v||.

If P₁ = (-2, 3), P₂ = (-1, 5), and v is the vector from P₁ to P₂, Write v in terms of i and j.

In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = 3i + j

In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = i - j

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.