The equation,
projx⃗y⃗=x⃗⋅y⃗|x⃗|x⃗|x⃗|projx→y→=x→⋅y→|x→|x→|x→|
Holds for any vectors we can let those be πa⃗πa→andeb⃗eb→. Where ππ and ee are some random constants like −2−2 and 33.
projπa⃗eb⃗=πa⃗⋅eb⃗|πa⃗|πa⃗|πa⃗|projπa→eb→=πa→⋅eb→|πa→|πa→|πa→|
Now usea⃗⋅(cb⃗)=ca⃗⋅b⃗a→⋅(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→|=
.
