Vectors

Question 1

Position vector

Answer 1

When a point p in space (x, y, z) is represented by a vector.

Question 2

Vector field

Answer 2

Associates a unique vector with every point in space. For instance, a vector field in the plane can be visualized as a collection of arrows with a given magnitude and direction, each attached to a point in the plane.

Ex: vectors assigned at positions (0,1), (1,1), etc. can include electric, magnetic fields.

Question 3

Parametric representations and tangent vectors

Answer 3

A family of vectors can be expressed as a function of a single variable, ex time, called a parameter. The derivative of that function with respect to a parameter is called a tangent vector.

Question 4

the dot product of two mutually perpendicular vectors

Answer 4

it’s zero.

Question 5

Parallel vectors have components that are …

Answer 5

Proportional.

Question 6

If the dot product of two vectors equals 0, the vectors are …..?

Answer 6

Mutually perpendicular.

Question 7

the angle btn two curves is the angle btn their ___?

Answer 7

Tangent vectors.