Bantu jawab soal vektor

Bantu jawab soal vektor

Jawab:

Penjelasan dengan langkah-langkah:

$a) ; bold{widehat{a}} = dfrac{bold{a}}{bold{|| a ||}} = dfrac{3widehat{i}+widehat{j}}{sqrt{3^2+1^2}} = dfrac{3widehat{i}+widehat{j}}{sqrt{10}} = dfrac{3}{sqrt{10}}; widehat{i}+dfrac{1}{sqrt{10}}; widehat{j}\b) ; bold{widehat{2b}} = bold{widehat{b}} = dfrac{bold{b}}{bold{|| b ||}} = dfrac{widehat{i}-2widehat{j}}{sqrt{2^2+1^2}} = dfrac{widehat{i}-2widehat{j}}{sqrt{5}} = dfrac{1}{sqrt{5}}; widehat{i}-dfrac{2}{sqrt{5}}; widehat{j}\$

$c) ; bold{widehat{a-2b}} = dfrac{bold{a-2b}}{bold{|| a-2b ||}} = dfrac{widehat{i}+5widehat{j}}{sqrt{5^2+1^2}} = dfrac{widehat{i}+5widehat{j}}{sqrt{26}} = dfrac{1}{sqrt{26}}; widehat{i}+dfrac{5}{sqrt{26}}; widehat{j}$

$displaystyle theta = cos^{-1}left( frac{bold{abullet b}}{bold{|| a || cdot || b ||}} right)\\theta = cos^{-1}left( frac{3cdot2+ 1cdot 3+2cdot (-1)}{sqrt{3^2+1^2+2^2} cdot sqrt{2^2+3^2+1^2}} right)\\boxed{boxed{theta = cos^{-1}left( frac{1}{2} right) = dfrac{pi}{3}}}$