Vector Components and Angles

The video tutorial explains how to find the component form of vectors given their magnitude and direction. It covers vectors along the negative y-axis and positive x-axis, using trigonometry and the unit circle to calculate components. The tutorial provides examples and emphasizes understanding vector direction and magnitude.

What is the magnitude of vector v when it lies along the negative y-axis?

• 4.5

• 6.5

• 3.5

• 5.5

What is the angle in standard position for a vector lying along the negative y-axis?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

Why is the x-component of a vector along the negative y-axis zero?

• Because the vector is at 90 degrees

• Because there is no horizontal change

• Because there is no vertical change

• Because the vector is at 45 degrees

What is the y-component of a vector with a magnitude of 5.5 along the negative y-axis?

• 0

• -5.5

• 5.5

• 1

What is the cosine of 270 degrees?

• -1

• 0

• 1

• 0.5

What is the sine of 270 degrees?

• 0

• 1

• -1

• 0.5

What is the magnitude of vector v when it lies along the positive x-axis?

• 8

• 7

• 6

• 5

What is the angle in standard position for a vector lying along the positive x-axis?

• 180 degrees

• 90 degrees

• 0 degrees

• 270 degrees

Why is the y-component of a vector along the positive x-axis zero?

• Because the vector is at 45 degrees

• Because there is no horizontal change

• Because there is no vertical change

• Because the vector is at 90 degrees

What is the cosine of 0 degrees?

• 0

• 0.5

• -1

• 1