vectors in plane

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

Question 1

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

Question 2

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

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 $\vec{AB}$ ?

Question 4

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

Question 5

How can the norm of a vector be determined ?

Question 6

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

Question 7

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

Question 8

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

Question 9

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

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