How do i calculate this dot product

[vande060]

Homework Statement

i dot 1/√2( i + j)

Homework Equations

The Attempt at a Solution

I think that perpendicular vectors are zero are dotted together, and parallel vectors dotted are 1. I am tempted do do the distributive property where i dot i is 1 and i dot j is zero, but I have a feeling this is not right

 

[rock.freak667]

i.i = 1

So you are essentially correct.

 

[gneill]

The dot product of two vectors with components (a,b,c) and (d,e,f) is simply the sum of the products of the corresponding components. In this case, a*d + b*e + c*f.

These vectors written in the form using unit vectors to represent the component directions are: ai + bj + ck, and di + ej + fk, where i,j,k are the unit vectors. The components are still (a,b,c) and (d,e,f).

It looks like your vectors are 2D vectors, (1,0) and (1/√2, 1/√2).