Learn how to write the vector in component form given magnitude and direction

The video tutorial explains how to solve word problems involving vectors by writing them in component form. It covers the process of expressing vectors using magnitude and direction, and demonstrates how to add vectors by simplifying their components. The tutorial uses examples to illustrate the concepts, including the use of trigonometric functions like cosine and sine to break down vectors into their components. The video also highlights the importance of the unit circle in evaluating vector points and provides a step-by-step guide to adding vectors in component form.

What is the formula for expressing a vector in component form using its magnitude and direction?

• V = magnitude of V times cosine of Theta I plus magnitude of V times sine of Theta J

• V = magnitude of V times sine of Theta I plus magnitude of V times cosine of Theta J

• V = magnitude of V times cosine of Theta J

• V = magnitude of V times sine of Theta I

How do you calculate the component form of vector U with a magnitude of 20 and an angle of 45 degrees?

• 20 times sine of 90 degrees, 20 times cosine of 90 degrees

• 20 times sine of 45 degrees, 20 times cosine of 45 degrees

• 20 times cosine of 45 degrees, 20 times sine of 45 degrees

• 20 times cosine of 90 degrees, 20 times sine of 90 degrees

What is the component form of vector V with a magnitude of 50 and an angle of 180 degrees?

• 50 times cosine of 90 degrees, 50 times sine of 90 degrees

• 50 times cosine of 180 degrees, 50 times sine of 180 degrees

• 50 times sine of 180 degrees, 50 times cosine of 180 degrees

• 50 times cosine of 0 degrees, 50 times sine of 0 degrees

When adding vectors in component form, what is the correct method?

• Subtract U1 from V1 and U2 from V2

• Multiply U1 by V1 and U2 by V2

• Add U1 to V1 and U2 to V2

• Divide U1 by V1 and U2 by V2

What is the final component form of the sum of vectors U and V?

• 10 sqrt 2, -50, 10 sqrt 2

• 10 sqrt 2, 50, 10 sqrt 2

• 20 sqrt 2, -50, 20 sqrt 2

• 20 sqrt 2, 50, 20 sqrt 2