Question

Para que um vetor u = (x, -1/2, 3/4), seja unitário qual deve ser o valor de x?

Answer 1

$\vec u = (x;- \frac{1}{2}; \frac{3}{4} )$

para que seja unitário |u| = 1

$|\vec u|= \sqrt{x^2+(- \frac{1}{2}^2)+( \frac{3}{4} )^2}=1 \\\\ \sqrt{x^2+( \frac{1}{4})+( \frac{9}{16})}=1 \\\\ \sqrt{x^2+ \frac{13}{16} } =1\\\\x^2+ \frac{13}{16}=1^2\\\\x^2=1- \frac{13}{16}\\\\x^2= \frac{3}{16}\\\\x= \pm\sqrt{ \frac{3}{16} }=\pm \frac{ \sqrt{3} }{ \sqrt{16} }= \pm\frac{ \sqrt{3} }{4}$