Vectors Q (1 Viewer)

[dsakvyilsa]

Hey, just need some help understanding the worked solution for this question. Thanks! (first image is Q, second is worked solution)

 

[dsakvyilsa]

the part that throws me off is the line where |b|^2 comes in, I can understand how they used it to get the solution but I don't understand where it actually came from.

 

[Masaken]

the part that throws me off is the line where |b|^2 comes in, I can understand how they used it to get the solution but I don't understand where it actually came from.

b.b = |b|^2
they're expanding it out but subbing that identity immediately

 

[5uckerberg]

I believe that in my memory this is where it comes from
.
This comes from the angle for vectors.
There, what you do is replace with and then what you will have is
.
The interesting part is that since lies in the same direction of then which leads to beccause . Note this is for two vectors going in the same direction.
For vectors going in the opposite direction
.

Vectors in this case are parallel and collinear.

 

[dsakvyilsa]

b.b = |b|^2
they're expanding it out but subbing that identity immediately

wait omg I didn't even notice that the brackets had two b's I thought they were 4 different terms for some reason damn