# Help with checking Vector Question

#### mathematicallyretarded

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

#### ojones

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

#### mathematicallyretarded

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

#### 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.

#### mathematicallyretarded

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!