Vectors and Scalars

Question 1

Vectors

Answer 1

Have both magnitude and direction.

Question 2

Scalars

Answer 2

Have only magnitude.

Question 3

When multiplying two vectors, if the answer is a scalar (e.g., work), then what do you do next? (mathematically)

Answer 3

Multiply the vector product by COSθ
e.g., W = Fd(COSθ), a.k.a. the scalar or dot product
θ : the angle between the two vectors

Question 4

When multiplying two vectors, if the answer is a third vector (e.g., torque), what do you do next, mathematically?

Answer 4

Multiply by sinθ

e.g., T = Fr(sinθ), a.k.a. the “vector” or “cross” product

Question 5

If an angle is measured with respect to the x-axis, what equation gives the x-component and what equation gives the y-component?

Answer 5

The x-component is given by V(cosθ)
The y-component is given by V(sinθ)

V = magnitude of the original vector

Question 6

If an angle is measured with respect to the y-axis, what equation gives the x-component and what equation gives the y-component?

Answer 6

The x-component is given by V(sinθ)
The y-component is given by V(cosθ)

INVERSE RELATIONSHIP WITH IF THE ANGLE IS MEASURED WITH RESPECT TO THE X-AXIS!