Selftest: Simple arithmetic operations

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Exercises for chapter Vector algebra | Article: Simple arithmetic operations

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1. Which of the following vectors forms the sum of $\vec{\mathbf{a}}$ and $\vec{\mathbf{b}}$?

	$\begin{pmatrix} 0 \\ 6 \end{pmatrix}$
	$\begin{pmatrix} 2 \\ 3 \end{pmatrix}$
	$\begin{pmatrix} 5 \\ 0 \end{pmatrix}$
	$\begin{pmatrix} -2 \\ 3 \end{pmatrix}$
→	The x-components of the two vectors cancel each other. Therefore the sum vector only has an y-component unequal zero. The length is the sum of the two y-components. Further information: see Simple arithmetic operations

2. Which of the following vectors forms the sum of $\vec{\mathbf{a}}$ and $\vec{\mathbf{b}}$?

	$\begin{pmatrix} -5 \\ 6 \end{pmatrix}$
	$\begin{pmatrix} -2 \\ 0 \end{pmatrix}$
	$\begin{pmatrix} 0 \\ -3 \end{pmatrix}$
	$\begin{pmatrix} -6 \\ 5 \end{pmatrix}$
→	Vector $\vec{\mathbf{a}}$ only has an x-component, vector $\vec{\mathbf{b}}$ in contrast only has a y-component. The resulting vector consists of the x-component of $\vec{\mathbf{a}}$ and the y-component of $\vec{\mathbf{b}}$. Further information: see Simple arithmetic operations

3. Which of the following vectors forms the sum of $\vec{\mathbf{a}}$ and $\vec{\mathbf{b}}$?

	$\begin{pmatrix} 0 \\ 6 \end{pmatrix}$
	$\begin{pmatrix} 2 \\ 3 \end{pmatrix}$
	$\begin{pmatrix} 3 \\ 4 \end{pmatrix}$
	$\begin{pmatrix} -4 \\ 3 \end{pmatrix}$
→	The x-component of vector $\vec{\mathbf{a}}$ is directed opposite to the x-component of vector $\vec{\mathbf{b}}$. So the x-components are substracted. The y-components are added as usual. Further information: see Simple arithmetic operations

4. Which of the following vectors forms the substraction $\vec{\mathbf{a}}-\vec{\mathbf{b}}$?

	$\begin{pmatrix} 0 \\ -6 \end{pmatrix}$
	$\begin{pmatrix} 7 \\ -3 \end{pmatrix}$
	$\begin{pmatrix} 0 \\ 6 \end{pmatrix}$
	$\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}$
→	Because the x-components are equal, the resulting x-component is zero. The y-component of the resulting vector is the substraction of the y-components. Further information: see Simple arithmetic operations

5. Which of the following vectors forms the substraction $\vec{\mathbf{a}}-\vec{\mathbf{b}}$?

	$\begin{pmatrix} 3 \\ 0 \end{pmatrix}$
	$\begin{pmatrix} -2 \\ -3 \end{pmatrix}$
	$\begin{pmatrix} 4 \\ -2 \end{pmatrix}$
	$\begin{pmatrix} -4,5 \\ 2 \end{pmatrix}$
→	The substraction of vectors can be traced back to vector addition because $\vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}})$. Further information: see Simple arithmetic operations

6. Which of the following vectors forms the substraction $\vec{\mathbf{a}}-\vec{\mathbf{b}}$?

	$\begin{pmatrix} 0 \\ -6 \end{pmatrix}$
	$\begin{pmatrix} 3 \\ -3 \end{pmatrix}$
	$\begin{pmatrix} 0 \\ 8 \end{pmatrix}$
	$\begin{pmatrix} -2,5 \\ 0,5 \end{pmatrix}$
→	Because the x-components are equal, the resulting x-component is zero. The y-component of the resulting vector is the substraction of the y-components. Further information: see Simple arithmetic operations

7. Which statement is true?

	For the calculation of the difference vector $\vec{\mathbf{a}}-\vec{\mathbf{b}}$ first the vector $-\vec{\mathbf{a}}$ is formed by inverting the direction of $\vec{\mathbf{a}}$.
	For the calculation of the difference vector $\vec{\mathbf{a}}-\vec{\mathbf{b}}$ first the vector $-\vec{\mathbf{b}}$ is formed by inverting the direction of $\vec{\mathbf{a}}$.
	For the calculation of the difference vector $\vec{\mathbf{a}}-\vec{\mathbf{b}}$ first the vector $-\vec{\mathbf{b}}$ is formed by inverting the direction of $\vec{\mathbf{b}}$.
→	The substraction of vectors can be traced back to vector addition because $\vec{\mathbf{a}}-\vec{\mathbf{b}}=\vec{\mathbf{a}}+(-\vec{\mathbf{b}})$. Further information: see Simple arithmetic operations

8. Fill-in-the-blank text:

Fill in the following words:

negative value, same direction, zero vector, factor

Multiplying a vector $\vec{\mathbf{a}}$ by a real value p results in a vector $\vec{\mathbf{a}}_p$ with and different magnitude. The magnitude changes with ${p}$. If the resulting vector $\vec{\mathbf{a}}_p$ has an oppsite direction, p is a . The special case p=0 results in a .

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