Calculating several linear combinations of three 3-dimensional vectors. 

Calculating several linear combinations of three 2-dimensional vectors. 

This easy question is intended to be used by administrators to test the integration of Numbas with a learning environment.

Calculate the magnitude of a 3-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j + v_3 \mathbf k$.

Calculate the magnitude of a 3-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v_1\\v_2\\v_3}$.

Calculate the magnitude of a 2-dimensional vector $\mathbf v$, where $\mathbf v$ is written in the form $v_1 \mathbf i+v_2 \mathbf j$.

Calculate the magnitude of a 2-dimensional vector, where $\mathbf v$ is written in the form $\pmatrix{v1\\v2}$.

Given the position vectors of three 2-dimensional points $A$, $B$ and $C$, find the coordinates of a fourth point $D$ such that $ABCD$ forms a parallelogram. 

Find the unit vectors in the direction of four 2-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Equilibrium of a rigid body.  Find tension to raise a pole.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Skills Audit for Maths and Stats for MAS005 Science and Engineering Foundation Year students who have already studied A-level maths.

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Find the determinant of a random (2x2) matrix.

Determine the reactions supporting a cantilever beam carrying concentrated forces and moments.

The student is shown a circuit diagram with three logic gates. It's always in the form (a OP b) OP (b OP c).

They have to fill in a truth table for the circuit. There is a step which expands the truth table, adding a column for each of the first two gates.

Draws a triangle based on 3 side lengths and randomises asking for hypotenuse or not.

Multiple choice: select the correct (mxn) representation of the sizes of various matrices.

Calculating the derivative of a function of the form $(ax+b)^n$ using the chain rule.

Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Simple exercise in collecting terms in different powers of \(x\)

Calculate the product of two 3D vectors in column notation.

Find the cross product of 2D vectors (WARNING: requires scalar answer (magnitude only))

Part 1: multiply a 3D vector by an integer scalar
Part 2: perform scalar multiplication and subtraction in one expression with two 3D vectors

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Homework set.  Problems involving two interacting particles.

Homework set.  Variations on problems involving single particle equilibrium.

Homework set.  Vector addition in two dimensions by summing scalar components.