Help with checking Vector Question

Hey guys I am not sure if this is the right thread (can't seem to find one for vectors) but i am not sure if i'm on the right track here so i need some advice

Question is:

if \(\displaystyle \vec{a}=3i-2j\) , \(\displaystyle \vec{b}=-4i+4j\) , and \(\displaystyle \vec{c}=6i+-9j\) express the following vectors in their simplest form:

(i)\(\displaystyle -5\vec{b}\)
(ii)\(\displaystyle 2\vec{a}-\frac{1}{2}\vec{c}\)
(iii)\(\displaystyle \frac{2}{3}\vec{a}-\frac{1}{2}\vec{b}-\frac{1}{4}\vec{c}\)

My Solution:

(i) \(\displaystyle -5\left(-4i+4j \right)=20i+\left(-20j \right)\)
(ii) \(\displaystyle 2(3i-2j)-\frac{1}{2}(6i+(-9)j)\)
\(\displaystyle = 6i-4j-3i+(-\frac{9}{2})j\)
\(\displaystyle = (6-3=3i) -4j-\frac{9}{2}\)
\(\displaystyle = -\frac{4}{1}-\frac{9}{2}\)
\(\displaystyle =-\frac{8}{2}-\frac{9}{2}\)
\(\displaystyle =-\frac{17}{2}\)

Answer? \(\displaystyle 3i-\frac{17}{2}j\)

(iii) \(\displaystyle \frac{2}{3}(3i-2j)-\frac{1}{2}(-4i+4j)-\frac{1}{4}(6i+(-9)j)\)
\(\displaystyle (2i-\frac{4}{3}j)-(-2i+2j)-(\frac{3}{2}i+(-\frac{9}{4}j)\)
\(\displaystyle 2i+2i-\frac{3}{2}i\)
\(\displaystyle = \frac{4}{1}i+\frac{3}{2}i\)
\(\displaystyle = \frac{8}{2}+\frac{3}{2}\)
\(\displaystyle =\frac{11}{2}i\)

\(\displaystyle -\frac{4}{3}j+\frac{2}{1}j-\frac{9}{4}j\)
\(\displaystyle = -\frac{16}{12}j+\frac{24}{12}j-\frac{27}{12}j\)
\(\displaystyle = -\frac{19}{12}j\)

Answer? \(\displaystyle \frac{11}{2}i-\frac{19}{12}j\)
 
May 2010
274
67
Los Angeles, California
Looks Ok to me but you're presentation was hard to follow.
 
May 2010
274
67
Los Angeles, California
Actually, there is an arithmetic error in (ii): answer should be \(\displaystyle 3{\bf i}+(-4+\frac{9}{2}){\bf j}=3{\bf i}+\frac{1}{2}{\bf j}\)

(iii) also has an error: you changed \(\displaystyle -\frac{3}{2}{\bf i}\) to \(\displaystyle \frac{3}{2}{\bf i}\) by mistake.
 
Actually, there is an arithmetic error in (ii): answer should be \(\displaystyle 3{\bf i}+(-4+\frac{9}{2}){\bf j}=3{\bf i}+\frac{1}{2}{\bf j}\)

(iii) also has an error: you changed \(\displaystyle -\frac{3}{2}{\bf i}\) to \(\displaystyle \frac{3}{2}{\bf i}\) by mistake.
ah yea thanks! Great pickup!