Vector Components and Magnitude

The video tutorial explains how to find the component form of a vector given its magnitude and direction. It covers the process of determining the vector's components using trigonometry, specifically focusing on a vector in the second quadrant making a 45-degree angle with the positive y-axis. The tutorial includes sketching the vector, using trigonometric functions to solve for the x and y components, and calculating exact values using a reference triangle and the unit circle.

What is the magnitude of vector v?

• 3

• 3√3

• 6

• √3

In which quadrant does vector v lie?

• Fourth

• Third

• Second

• First

What is the angle in standard position for vector v?

• 45 degrees

• 90 degrees

• 180 degrees

• 135 degrees

How do you calculate the x component of vector v?

• Magnitude times sine of angle

• Magnitude times cosine of angle

• Magnitude divided by sine of angle

• Magnitude divided by cosine of angle

What is the cosine of 135 degrees?

• √2/2

• -√2/2

• 1/2

• -1/2

What is the sine of 135 degrees?

• 1/2

• √2/2

• -1/2

• -√2/2

What is the x component of vector v?

• -3√3/2

• 3√6/2

• -3√6/2

• 3√3/2

What is the y component of vector v?

• -3√6/2

• 3√6/2

• 3√3/2

• -3√3/2

Why can't the 6 and 2 be simplified in the final component form?

• Because they are not under the square root

• Because 6 is under the square root

• Because 2 is under the square root

• Because they are both under the square root

What is the final component form of vector v?

• (-3√3/2, -3√3/2)

• (3√6/2, -3√6/2)

• (3√3/2, 3√3/2)

• (-3√6/2, 3√6/2)