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 $\pmatrix{v1\\v2}$.

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

Question requires students to interchange units of Hz with MHz, GHz, THz. Question is not very efficient at present- frequencies spanning many orders of magnitude are generated by variables in a clumsy way. Could be improved by having frequency generated by a 10^((random(1000..4000)/1000) variable instead, for example. 

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Given three vectors with integer components, find the corresponding magnitude and direction.

Find the magnitude and direction of a force given its scalar components.

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

Two forces act on a bell crank. This problem has two unknown magnitudes and an unknown direction which makes it tricky to solve by the equilibrium equation method.  

The solution is much simpler if three force body principle is used.

Two known forces, and a third with known magnitude act on a rigid body.  Apply $\Sigma M = 0$ about a pin restraint to determine the direction of the third force.  The problem has two valid answers.

Given three vectors, arrange them in a tip to tail arrangement using geogebra, then estimate the magnitude and direction of their resultant.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Translating prefixes into orders of magnitude, e.g. kilo = 10^(3)

Stating orders of magnitude for real-world values, e.g. height of Everest, diameter of a atom.

Finding a vector when given the magnitude of the vector and a parallel vector.

Evaluación de la superposición vectorial de campos provenientes de cuatro cargas puntuales. Este es un problema de suma de vectores, magnitudes de vectores y productos escalares (puntos) con un poco de trigonometría.

Convert a metric measurement to another order of magnitude, e.g. g to kg.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Questions which ask the student to intepret vector diagrams in order to write out the components in terms of base vectors. Also addition and subtraction of vectors and vector magnitude.

This question introduces base vectors i and j and asks the student to interpret a JSXGraph diagram to write four vectors in terms of the base vectors. Further parts ask the student to add vectors and find a magnitude.

This question asks the student to interpret a JSXGraph diagram to write three vectors in terms of the base vectors. Each vector has both a horizontal and vertical component. Further parts ask the student to add vectors and find a magnitude. 

Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.

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