11/28/22 - Vectors

Question 1

What is a vector?

Answer 1

A quantity with direction and magnitude

Question 2

What quality of a vector corresponds to the length of the arrow?

Answer 2

Magnitude ||v||

Question 3

What is the difference between a scalar and a vector?

Answer 3

Both have magnitude, but a scalar does not have direction

Question 4

How do you add vectors that form a right triangle?

Answer 4

Use the Pythagorean Theorem. The sum of the vectors will be the triangle’s hypotenuse. Each side length is the magnitude of a vector.

Question 5

How do you add vectors that form a non-right triangle?

Answer 5

Law of Cosines or Law of Sines

Question 6

What is a unit vector?

Answer 6

A vector with a length (magnitude) of 1

Question 7

What are the two standard unit vectors?

Answer 7

Vector i, goes in the positive x direction (right)
Vector j, goes in the positive y direction (up)

Question 8

For a vector v, what is the unit vector decomposition?

Answer 8

v = a(i) + b(j)
a and b are scalars

Question 9

If vector u = a(i) + b(j), what is ||u||?

Answer 9

||u|| = √(a^2 + b^2)

Question 10

If vector v makes an angle θ with the horizontal axis, what is the equation for the vector?

Answer 10

v = ||v||cosθ(i) + ||v||sinθ(j)