Question

Vectors u and v are shown on the graph.

Part A: Write u and v in component form. Show your work. (3 points)

Part B: Find u + v. Show your work. (2 points)

Part C: Find 5u − 2v. Show your work. (5 points)

Answer 1

Part A: Write u and v in component form.

Vector U: u = (-6, 8)

Vector V: v = (17, 8)

In the component form, a vector is represented as an ordered pair (x, y), where 'x' is the horizontal component (the value along the x-axis) and 'y' is the vertical component (the value along the y-axis).

Part B: Find u + v.

To find the sum of vectors U and V, simply add their corresponding components:

u + v = (-6, 8) + (17, 8) = (-6 + 17, 8 + 8) = (11, 16)

So, the result of u + v is the vector (11, 16).

Part C: Find 5u − 2v.

To find the scalar multiplication of vectors U and V, multiply each component by the scalar:

5u = 5 * (-6, 8) = (-30, 40)

2v = 2 * (17, 8) = (34, 16)

Now, subtract 2v from 5u:

5u - 2v = (-30, 40) - (34, 16) = (-30 - 34, 40 - 16) = (-64, 24)

So, the result of 5u - 2v is the vector (-64, 24).