- Purpose
- Getting Started
- Background
- Angle between two vectors
- Vector Projection
- Area of a Triangle
- Exercises

The purpose of this lab is to use Maple to introduce you to a number of useful commands for working with vectors, including some applications. The commands come from the Maple `linalg` and `CalcP7` packages which must be loaded before any of its commands can be used.

To assist you, there is a worksheet associated with this lab that you can copy into your home directory by going to your computer's start menu and choose run. In the run field type:

\\storage\academics\math\calclab

when you hit enter, you can then choose MA1023 and then choose the worksheet

Vector_start_B14.mw

Remember to immediately save it in your own home directory. Once you've copied and saved the worksheet, read through the background on the internet and the background of the worksheet before starting the exercises.

Computes the dot product (also known as the inner product) of two vectors.

Computes the cross product of two vectors.

Evaluates expressions involving vectors (and matrices).

Computes the norm, or length, of a vector.

The scalar component of in the direction of can be found using the following formula:

A unit vector perpendicular to the plane containing points , and is given by .

- Given the vectors
and
, and
, use Maple to compute the numeric value of the following expressions, if possible. For those that cannot be computed because they make no sense, please explain what is wrong.
- Find the angle between each of the vectors above.
- Find a vector perpendicular to such that

where and . Then show that and are perpendicular. - Find the equation of the line through the point and parallel to the vector
. Plot the line and vector on the same graph.
- For the vectors
and
, find the vector projection of onto and the scalar component of in the direction of .
- Find the area of the triangle with vertices , and . (Hint: Shift the triangle to the origin by representing two of the sides of the triangles with vectors in standard form.) Also, find a unit vector perpendicular to the plane containing these three points.

2014-12-10