# Thread: Help with checking Vector Question

1. ## 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? $\displaystyle \frac{11}{2}i-\frac{19}{12}j$

2. Looks Ok to me but you're presentation was hard to follow.

3. Originally Posted by ojones
Looks Ok to me but you're presentation was hard to follow.
ah thank you! i'll write it better in my maths book and write it better next time i need help on here

4. 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.

5. Originally Posted by ojones
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!