- Used to define a vector.
- Computes the dot product of two vectors.
- Computes the cross product of two vectors.
- Evaluates expressions involving vectors.
- Computes the norm, or length of a vector. For reasons explained below, the use of this commmand is not recommended. A better alternative for our purposes is to use the square root of the dot product of a vector with itself.

> with(linalg): > a := [2, 13, -6]; > b := [5, -4, 17]; > a+b; > 5*a-2*b; > dotprod(a,b); > crossprod(a,b); > crossprod(b,a); > dotprod(a,crossprod(a,b));The next two commands show two different ways to compute the length of a vector. The first way uses the

> norm(a,2); > sqrt(dotprod(a,a));The final example for fixed vectors shows two methods for computing the vector projection or component of

> a_unit := evalm(a/sqrt(dotprod(a,a))); > comp_a1 := evalm(dotprod(b,a_unit)*a_unit);The second method uses the formula for the component.

> comp_a2 := evalm(dotprod(b,a)/dotprod(a,a)*a);

- Given the vectors
compute the following:
- a)
- b)

- Given the following triangle
with the points
,, and
- a)
- Show that the triangle is a right triangle using the dot product.
- b)
- Find the area of the triangle using the cross product.

2006-09-27