Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?
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Answer:
[tex]-\frac{2}{3}i - \frac{13}{5}j[/tex]
Step-by-step explanation:
-0.4(3i + 4i) - 0.3(-2i + 5j) + 0.2(-[tex]\frac{1}{3}i[/tex] + [tex]\frac{5}{2}[/tex]j)
-1.2i - 1.6j + 0.6i - 1.5j - [tex]\frac{0.2}{3}[/tex]i + 0.5j
Converting to fraction form;
[tex]-\frac{6}{5}i + \frac{3}{5}i - \frac{1}{15}i - \frac{8}{5}j - \frac{3}{2}j + \frac{1}{2} j[/tex]
Solving the i part;
[tex]\frac{-18i + 9i - i}{15}[/tex] = [tex]-\frac{2}{3}i[/tex]
Solving the j part;
[tex]\frac{-16j-15j+5j}{10} = -\frac{13}{5}[/tex]j
So -0.4a - o.3b + 0.2d = [tex]-\frac{2}{3}i[/tex] - [tex]\frac{13}{5}j[/tex]