Answer:
Please check the explanation.
Step-by-step explanation:
Given the vector
v = 6i + 2√3j
The Magnitude of a vector:
[tex]\mathrm{Computing\:the\:Euclidean\:Length\:of\:a\:vector}:\quad \left|\left(x_1\:,\:\:\ldots \:,\:\:x_n\right)\right|=\sqrt{\sum _{i=1}^n\left|x_i\right|^2}[/tex]
[tex]=\sqrt{6^2+\left(2\sqrt{3}\right)^2}[/tex]
[tex]=\sqrt{36+12}[/tex]
[tex]=\sqrt{48}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]=\sqrt{3}\sqrt{2^4}[/tex]
[tex]=4\sqrt{3}[/tex]
The Direction of a vector:
tan Ф = y/x
y=2√3
x = 6
tan Ф = y/x
= 2√3 / 6
= √3 / 3
[tex]\theta \:=tan\:^{-1}\left(\frac{\sqrt{3}}{3}\right)[/tex]
[tex]\:\theta \:=\frac{\pi \:}{6}=30^{\circ \:}[/tex]
