5.1

Figure 5.1 : vectors in $\mathbb{R}^2$

Question 1

How many coordinates does $\vec{v}$ have ?

$\vec{v} = \begin{pmatrix} -13 \\ 10 \\ 21 \\ -34 \\ \end{pmatrix}$

$5\times4$

$4$

$5$

$1\times4$

Question 2

What are the coordinates of ${\color{violet}{\vec{w}}}$ (see Figure 5.1) ?

$(1,0)$

$(0,-1)$

$(2,1)$

$(-2,0)$

Question 3

Let be the points $A=\left(\begin{smallmatrix} 120 \\ -122 \end{smallmatrix}\right)$ and $B= \left(\begin{smallmatrix} -100 \\ 105 \end{smallmatrix}\right)$. What are the coordinates of the vector $\vec{AB}$ ?

$(120,-17)$

$(220,-122)$

$(120,305)$

$(-220,227)$

Question 4

What ${\color{orange}{\vec{e}}} – {\color{violet}{\vec{w}}}$ is equal to (see Figure 5.1) ?

${\color{navy}{\vec{n}}}$

${\color{red}{\vec{t}}}$

${\color{grey}{\vec{m}}}$

${\color{darkcyan}{\vec{s}}}$

Question 5

How can the norm of a vector be determined ?

Dirac’s equation

Cauchy-Schwarz inequality

Pythagoras’s theorem

Euler’s formula

Question 6

What is the length of ${\color{darkcyan}{\vec{s}}}$ (see Figure 5.1) ?

$5$

$\sqrt{3}$

$17$

$\sqrt{17}$

Question 7

What is the value of $\lambda$ such as $\lambda{\color{violet}{\vec{w}}} – {\color{grey}{\vec{m}}} = \left(\begin{smallmatrix} 0 \\ 0 \end{smallmatrix}\right)$ (see Figure 5.1) ?

$\frac{1}{2}$

$2$

$-2$

$\frac{-1}{2}$

Question 8

Which vector is collinear to ${\color{purple}{\vec{u}}}$ (see Figure 5.1) ?

${\color{red}{\vec{t}}}$

${\color{grey}{\vec{m}}}$

${\color{green}{\vec{p}}}$

${\color{darkcyan}{\vec{s}}}$

Question 9

Let $\vec{g}= \left(\begin{smallmatrix} 5 \\ 7 \end{smallmatrix}\right)$. Which vector is collinear to $\vec{g}$ ?

$\left(\begin{smallmatrix} -100 \\ 121 \end{smallmatrix}\right)$

$\left(\begin{smallmatrix} -35 \\ 49 \end{smallmatrix}\right)$

$\left(\begin{smallmatrix} -49 \\ -25 \end{smallmatrix}\right)$

$\left(\begin{smallmatrix} -30 \\ -42 \end{smallmatrix}\right)$