202109161039 Exercises 1.1.A (Q1)

Calculate the magnitudes of the following vectors:

(a) $\mathbf{v}=(2,-1)$
(b) $\mathbf{v}=(2,-1,0)$
(c) $\mathbf{v}=(3,2,-2)$
(d) $\mathbf{v}=(0,0,1)$
(e) $\mathbf{v}=(6,4,-4)$

Solution.

(a)

$\begin{aligned} v & = |\mathbf{v}| \\ & = \sqrt{(2)^2+(-1)^2} \\ & = \sqrt{5} \end{aligned}$

(b)

$\begin{aligned} v & = |\mathbf{v}| \\ & = \sqrt{(2)^2+(-1)^2+(0)^2} \\ & = \sqrt{5} \end{aligned}$

(c)

$\begin{aligned} v & = |\mathbf{v}| \\ & = \sqrt{(3)^2+(2)^2+(-2)^2} \\ & = \sqrt{17} \end{aligned}$

(d)

$\begin{aligned} v & = |\mathbf{v}| \\ & = \sqrt{(0)^2+(0)^2+(1)^2} \\ & = \sqrt{1} \\ & = 1 \end{aligned}$

(e)

$\begin{aligned} v & = |\mathbf{v}| \\ & = \sqrt{(6)^2+(4)^2+(-4)^2} \\ & = \sqrt{68} \\ & = 2\sqrt{17} \\ \end{aligned}$