Question

Vector u has an initial point at (3,9) and a terminal point at (-7,5). Vector v has an initial point at (1, -4) and a terminal point at (6, -1). What is u + v in component form?

A) (-10, -4)
B) (-5, -1)
C) (3, 9)
D) (5, 3)

Answer 1

To find the sum of two vectors in component form, subtract the initial point coordinates from the terminal point coordinates for both vectors and then add the corresponding components. The sum of vectors u and v in component form is (-5, -1), which is option B.

Step-by-step explanation:

To find the sum of the vectors u and v in component form, we first need to determine the components of each vector individually. For vector u, the components can be found by subtracting the initial point from the terminal point:

• ux = (-7) - (3) = -10
• uy = (5) - (9) = -4

Similarly, for vector v:

• vx = (6) - (1) = 5
• vy = (-1) - (-4) = 3

The sum of the two vectors in component form is then:

• (u + v)x = ux + vx = -10 + 5 = -5
• (u + v)y = uy + vy = -4 + 3 = -1

The vector u + v is therefore in component form (-5, -1). The correct answer is option B) (-5, -1).