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# PLZ help asap!!! (repost)

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Let v and w be vectors such that $${proj}_{{w}}({v} )= \begin{pmatrix} 4 \\ -7 \end{pmatrix}$$.

Find $$\operatorname{proj}_{-2 {w}} (3 {v})$$.

Oct 11, 2019

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The equation,

$$projx⃗ y⃗ =x⃗ ⋅y⃗ |x⃗ |x⃗ |x⃗ |projx→y→=x→⋅y→|x→|x→|x→|$$

Holds for any vectors we can let those be $$πa⃗ πa→ and eb⃗ eb→$$. Where ππ and ee are some random constants like −2−2 and 33.

$$projπa⃗ eb⃗ =πa⃗ ⋅eb⃗ |πa⃗ |πa⃗ |πa⃗ |projπa→eb→=πa→⋅eb→|πa→|πa→|πa→|$$

Now use$$a⃗ ⋅(cb⃗ )=ca⃗ ⋅b⃗ a→⋅(cb→)=ca→⋅b→ and |cw⃗ |=c|w⃗ ||cw→|=c|w→|.$$ To get

e(pro j base a to the power of b) is the answer because

$$π2eπ2a⃗ ⋅b⃗ |a⃗ |a⃗ |a⃗ |=π2eπ2a→⋅b→|a→|a→|a→| =$$

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Oct 11, 2019
edited by SVS2652  Oct 11, 2019