You will often see proj (Vector a onto Vector b) written as proj b⃗ a⃗ .Show that projb⃗ a⃗ =(a⃗ ⋅b⃗ b⃗ ⋅b⃗ )b⃗ .

Answer 1

Your notation is a mystery to me.
The magnitude of the projection of A on to A is |A| cos T
where T is the angle between A and B
but |A| cos T = |A| |B| cos T /|B|
which is
A dot B /|B|
Now we need a unit vector in direction B
That is B/|B|
so in the end we need
A dot B * B /|B|^2

Answer 2

cxcxcx