Notes: `u = , v = ` Find the projection of u onto v. Then write u as the sum of the two orthogonal vectors, one of which is `proj

Sunday, 30 April 2017

$\displaystyle{u}=,{v}=$ Find the projection of u onto v. Then write u as the sum of the two orthogonal vectors, one of which is $\displaystyle{p}{r}{o}{j}_{{v}}{u}$ .

You need to evaluate the projection of vector u onto vector v using the formula, such that:

$\displaystyle{p}{r}{o}{j}_{{v}}{\left({u}\right)}={\left(\frac{{{u}\cdot{v}}}{{{{\left|{v}\right|}}^{{2}}}}\right)}\cdot{v}$

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

$\displaystyle{u}\cdot{v}={u}_{{x}}\cdot{v}_{{x}}+{u}_{{y}}\cdot{v}_{{y}}$

$\displaystyle{u}\cdot{v}={4}\cdot{1}+{2}\cdot{\left(-{2}\right)}$

$\displaystyle{u}\cdot{v}={4}-{4}$

$\displaystyle{u}\cdot{v}={0}$

$\displaystyle{p}{r}{o}{j}_{{v}}{\left({u}\right)}={\left(\frac{{0}}{{{{\left|{v}\right|}}^{{2}}}}\right)}\cdot{v}\Rightarrow{p}{r}{o}{j}_{{v}}{\left({u}\right)}={0}\cdot{v}\Rightarrow{p}{r}{o}{j}_{{v}}\ldots$

You need to evaluate the projection of vector u onto vector v using the formula, such that:

$\displaystyle{p}{r}{o}{j}_{{v}}{\left({u}\right)}={\left(\frac{{{u}\cdot{v}}}{{{{\left|{v}\right|}}^{{2}}}}\right)}\cdot{v}$

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

$\displaystyle{u}\cdot{v}={u}_{{x}}\cdot{v}_{{x}}+{u}_{{y}}\cdot{v}_{{y}}$

$\displaystyle{u}\cdot{v}={4}\cdot{1}+{2}\cdot{\left(-{2}\right)}$

$\displaystyle{u}\cdot{v}={4}-{4}$

$\displaystyle{u}\cdot{v}={0}$

$\displaystyle{p}{r}{o}{j}_{{v}}{\left({u}\right)}=<{0}\cdot{1},{0}\cdot{\left(-{2}\right)}>\Rightarrow{p}{r}{o}{j}_{{v}}{\left({u}\right)}=<{0},{0}>$

Hence, evaluating the projection of vector u onto vector v yields $\displaystyle{p}{r}{o}{j}_{{v}}{\left({u}\right)}=<{0},{0}>.$

Notes

Sunday, 30 April 2017

$\displaystyle{u}=,{v}=$ Find the projection of u onto v. Then write u as the sum of the two orthogonal vectors, one of which is $\displaystyle{p}{r}{o}{j}_{{v}}{u}$ .

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Is there any personification in "The Tell-Tale Heart"?

Sunday, 30 April 2017

Find the projection of u onto v. Then write u as the sum of the two orthogonal vectors, one of which is .

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Is there any personification in &quot;The Tell-Tale Heart&quot;?

$\displaystyle{u}=,{v}=$ Find the projection of u onto v. Then write u as the sum of the two orthogonal vectors, one of which is $\displaystyle{p}{r}{o}{j}_{{v}}{u}$ .

Is there any personification in "The Tell-Tale Heart"?