Hi, I really need help with the following problem and received an off topic reply on the past post. Please help!!!
Let v and w be vectors such that \({proj}_{{w}}({v} )= \begin{pmatrix} 4 \\ -7 \end{pmatrix}\).
Find \(\operatorname{proj}_{-2 {w}} (3 {v})\).
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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
\(π2eπ2a⃗ ⋅b⃗ |a⃗ |a⃗ |a⃗ |=π2eπ2a→⋅b→|a→|a→|a→| = \)
