Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given vectors $\boldsymbol{A}$ and $\boldsymbol{B}$, find their inner product.

When are vectors $\boldsymbol{A,\;B}$ perpendicular?

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

The students are given the magnitude and angle (in degrees) of a vector. They have to find its alpha and beta components.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

No description given

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Download a file and scan the values into R to obtain a numeric vector of values. Then use R to explore your numeric vector in order to find the answers to these questions.

$A,\;B$ $2 \times 2$ matrices. Find eigenvalues and eigenvectors of both. Hence or otherwise, find $B^n$ for largish $n$.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Construct a line in a GeoGebra worksheet by writing its definition string by hand.

This isn't a very neat way of doing this. It's easier to define two points in GeoGebra, then make a line through those points. You can set the positions of the points from Numbas using vectors.

List all vectors in a spanning set.

(repeated 3 times)

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

When are vectors $\boldsymbol{v,\;w}$ orthogonal?

Part b) is not answered in Advice, the given solution is for a different question.

Determine if various combinations of vectors are defined or not.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Find minimum distance between a point and a line in 3-space. The line goes through a given point in the direction of a given vector.

The correct solution is given, however the accuracy of 0.001  is not enough as in some cases answers near to the correct solution are also marked as correct.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Parametric form of a curve, cartesian points, tangent vector, and speed.

Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Questions on vector arithmetic and vector operations, including dot and cross product, as well as the vector equations of planes and lines.

Given a set of vectors, find a basis which generates their span as a subspace of $\mathbb{Z}_n$.

Given a matrix in the field $\mathbb{Z}_n$. By reducing it to row-echelon form (or otherwise), find a basis for the row space of the matrix, as a list of vectors.