Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

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

Find the unit vectors in the direction of four 3-dimensional vectors. Three of the vectors are given, and the fourth is expressed as a linear combination of two of the other vectors.

Calculating several linear combinations of three 3-dimensional vectors. 

Calculating several linear combinations of three 2-dimensional vectors. 

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.

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

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

Calculate the dot products of (a) two 2D vectors and (b) two 3D vectors.

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.  Vector addition in two dimensions by summing scalar components.

Homework set.  Find components of vectors in various situations.

Homwork Set.  Covers graphical, and trigonometric methods of vector addition.

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.

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Determine the resultant of three random 2-D vectors.  

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

Determine the oblique components of a vector.

Given the specifications of two vectors, draw the parallelogram representing their sum, then estimate length of the diagonal. 

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

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Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .

Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .

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