Length of projection without angle (1 Viewer)

Deem_Skills · Aug 27, 2022

Screen Shot 2022-08-27 at 7.54.10 pm.png

How would u do this?

NoMoreModernSR · Aug 27, 2022

Deem_Skills said:
View attachment 36151
How would u do this?

Umm bdo just do a dot b all divided by magnitude b times magnitude b and this fraction is multiplied by b

Lith_30 · Aug 27, 2022

we know that
$\\proj_\mathbf{b}\mathbf{a}=\frac{\mathbf{a}\cdot{\mathbf{b}}}{\mathbf{b}\cdot{\mathbf{b}}}\mathbf{b}\\\\=\frac{\mathbf{a}\cdot{\mathbf{b}}}{|\mathbf{b}|^2}|\mathbf{b}|\times\mathbf{\hat{b}}\\\\=\frac{\mathbf{a}\cdot{\mathbf{b}}}{|\mathbf{b}|}\mathbf{\hat{b}}$

As we can see here the magnitude of the projection is given by $\frac{\mathbf{a}\cdot{\mathbf{b}}}{|\mathbf{b}|}$ , cause $\mathbf{\hat{b}}$ is just a unit vector which means that the scalar multiple will be the magnitude of $proj_\mathbf{b}\mathbf{a}$ .

hence the length is
$\\\frac{10(1)-2(-7)}{\sqrt{1^2+7^2}}\\\\=\frac{24}{\sqrt{50}}\\\\=\frac{24}{5\sqrt{2}}\\\\=\frac{12\sqrt{2}}{5}$

Length of projection without angle (1 Viewer)

Deem_Skills

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NoMoreModernSR

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Lith_30

o_o

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