Question

Vector u has initial point at (3, 9) and terminal point at (–7, 5). Vector v has initial point at (1, –4) and terminal point at (6, –1).

What is u + v in component form?
⟨-10, -4⟩
⟨-5, -1⟩
⟨3, 9⟩
⟨5, 3⟩

Answer 1

⟨-5, -1⟩

Explanation:

Vector:

A vector is given by its endpoint subtracted by its initial point.

Vector u has initial point at (3, 9) and terminal point at (–7, 5)

Then

`u = (-7, 5) - (3,9) = (-7 - 3, 5 - 9) = (-10,-4)`

Vector v has initial point at (1, –4) and terminal point at (6, –1).

Then

`v = (6,-1) - (1,-4) = (6-1,-1-(-4)) = (5,3)`

What is u + v in component form?

`u + v = (-10,-4) + (5,3) = (-10+5,-4+3) = (-5,-1)`

⟨-5, -1⟩ is the answer.