Notes: `bbu = 2bbj, bbv = 3bbi` Find (a) `bbu + bbv`, (b) `bbu

Wednesday, 7 August 2013

$\displaystyle{\mathbf{{u}}}={2}{\mathbf{{j}}},{\mathbf{{v}}}={3}{\mathbf{{i}}}$ Find (a) $\displaystyle{\mathbf{{u}}}+{\mathbf{{v}}}$ , (b) $\displaystyle{\mathbf{{u}}}-{\mathbf{{v}}}$

You need to perform the addition of the vectors u and v, $\displaystyle{u}={u}_{{x}}\cdot{i}+{u}_{{y}}\cdot{j},{v}={v}_{{x}}\cdot{i}+{v}_{{y}}\cdot{j}$ , such that:

$\displaystyle{u}+{v}={\left({u}_{{x}}+{v}_{{x}}\right)}{i}+{\left({u}_{{y}}+{v}_{{y}}\right)}{j}$

$\displaystyle{u}+{v}={\left({0}+{3}\right)}{i}+{\left({2}+{0}\right)}{j}$

$\displaystyle{u}+{v}={3}{i}+{2}{j}$

Hence, evaluating the sum of the vectors u and v yields $\displaystyle{u}+{v}={3}{i}+{2}{j}$ .

You need to perform the difference of the vectors u and v, $\displaystyle{u}=\ldots$

You need to perform the addition of the vectors u and v, $\displaystyle{u}={u}_{{x}}\cdot{i}+{u}_{{y}}\cdot{j},{v}={v}_{{x}}\cdot{i}+{v}_{{y}}\cdot{j}$ , such that:

$\displaystyle{u}+{v}={\left({u}_{{x}}+{v}_{{x}}\right)}{i}+{\left({u}_{{y}}+{v}_{{y}}\right)}{j}$

$\displaystyle{u}+{v}={\left({0}+{3}\right)}{i}+{\left({2}+{0}\right)}{j}$

$\displaystyle{u}+{v}={3}{i}+{2}{j}$

Hence, evaluating the sum of the vectors u and v yields $\displaystyle{u}+{v}={3}{i}+{2}{j}$ .

You need to perform the difference of the vectors u and v, $\displaystyle{u}={u}_{{x}}\cdot{i}+{u}_{{y}}\cdot{j},{v}={v}_{{x}}\cdot{i}+{v}_{{y}}\cdot{j}$ , such that:

$\displaystyle{u}-{v}={\left({u}_{{x}}-{v}_{{x}}\right)}{i}+{\left({u}_{{y}}-{v}_{{y}}\right)}{j}$