Exploring Two-Dimensional Vectors

What is the result of adding the vectors (3, 4) and (1, 2)?

• (2, 3)

• (4, 6)

• (5, 6)

• (3, 5)

If vector A = (5, 2) and vector B = (3, -1), what is A - B?

• (8, 1)

• (2, -3)

• (3, 1)

• (2, 3)

Calculate the dot product of the vectors (2, 3) and (4, 1).

• 12

• 7

• 10

• 11

How do you resolve the vector (6, 8) into its components along the x and y axes?

• x-component: 6, y-component: 8

• x-component: 4, y-component: 8

• x-component: 6, y-component: 10

• x-component: 8, y-component: 6

What is the magnitude of the vector (3, 4)?

• 6

• 4

• 7

• 5

Determine the direction of the vector (1, 1) in degrees from the positive x-axis.

• 180 degrees

• 45 degrees

• 30 degrees

• 90 degrees

What is a unit vector in the direction of the vector (4, 3)?

• (0.5, 0.5)

• (0, 1)

• (1, 0)

• (0.8, 0.6)

If vector C = (2, 5), what are its components along the x and y axes?

• x-component: 2, y-component: 3

• x-component: 5, y-component: 2

• x-component: 0, y-component: 5

• x-component: 2, y-component: 5

Explain how vector addition can be applied in physics to find the resultant force.

• Vector addition is used to find the resultant force by summing the components of individual forces.

• Vector addition is only used in geometry, not physics.

• Resultant force can be found by multiplying individual forces together.

• Vector addition is irrelevant when calculating forces in a system.

What is the angle between the vectors (1, 0) and (0, 1)?

• 180 degrees

• 45 degrees

• 90 degrees

• 60 degrees