Problem 1

Determine whether or not the given points are collinear (that is, lie on a common straight line)

(a). , ,

They are not collinear as the vectors from the first to the second and the first to the third are not multiples of each other.

(b). , ,

They are collinear as the vectors from the first to the second and the first to the third are multiples of each other.

Problem 2

Determine whether the given pair of vectors is perpendicular

(a). ,

They are perpendicular

(b). ,

They are perpendicular

(c). ,

They are not perpendicular

Problem 3

Consider the vector

(a). Find a Unit Vector in the Same Direction as

(b). Find All Unit Vectors that Are Parallel to

(c). Find All Vectors that Are Parallel to and Have Length 10

(d). Find All Unit Vectors that Are Perpendicular to

Problem 4

Consider the vector

(a). Find a Unit Vector in the Same Direction as

(b). Find All Unit Vectors that Are Parallel to

(c). Find Four Different Unit Vectors that Are Perpendicular to

Problem 5

Let . Compute the projection of on and .