Notes: `bbu = , bbv = ` Find (a) `bbu + bbv`, (b) `bbu - bbv`, and (c) `2bbu

Monday, 29 May 2017

$\displaystyle{\mathbf{{u}}}=,{\mathbf{{v}}}=$ Find (a) $\displaystyle{\mathbf{{u}}}+{\mathbf{{v}}}$ , (b) $\displaystyle{\mathbf{{u}}}-{\mathbf{{v}}}$ , and (c) $\displaystyle{2}{\mathbf{{u}}}-{3}{\mathbf{{v}}}$ .

You need to evaluate the sum of two vectors, $\displaystyle{u}+{v}$ , hence you need to perform the addition of the same versors, such that:

$\displaystyle{u}=<{0},{0}>\Rightarrow{u}={0}{i}+{0}{j}$

$\displaystyle{v}=<{2},{1}>\Rightarrow{v}={2}{i}+{j}$

$\displaystyle{u}+{v}=<{0},{0}>+<{2},{1}>$

$\displaystyle{u}+{v}=<{0}+{2},{0}+{1}>\Rightarrow{u}+{v}=<{2},{1}>$

Hence, evaluating the sum $\displaystyle{u}+{v}$ yields $\displaystyle{u}+{v}=<{2},{1}>$

You...

You need to evaluate the sum of two vectors, $\displaystyle{u}+{v}$ , hence you need to perform the addition of the same versors, such that:

$\displaystyle{u}=<{0},{0}>\Rightarrow{u}={0}{i}+{0}{j}$

$\displaystyle{v}=<{2},{1}>\Rightarrow{v}={2}{i}+{j}$

$\displaystyle{u}+{v}=<{0},{0}>+<{2},{1}>$

$\displaystyle{u}+{v}=<{0}+{2},{0}+{1}>\Rightarrow{u}+{v}=<{2},{1}>$

Hence, evaluating the sum $\displaystyle{u}+{v}$ yields $\displaystyle{u}+{v}=<{2},{1}>$

You need to evaluate the difference of two vectors,u-v, hence you need to perform the subtraction of the same versors, such that:

$\displaystyle{u}-{v}=<{0},{0}>-<{2},{1}>$

$\displaystyle{u}-{v}=<{0}-{2},{0}-{1}>\Rightarrow{u}-{v}=<-{2},-{1}>$

Hence, evaluating the difference $\displaystyle{u}-{v}$ yields $\displaystyle{u}-{v}=<-{2},-{1}>.$

You need to evaluate the difference of the vectors, $\displaystyle{2}{u}-{3}{v}$ , hence you need to perform first the multiplication of each vector with the indicated scalar and then you need to perform the subtraction of the same versors, such that: