Because of the vector nature of Newton's second law the expressions for work and kinetic energy which we derived for one dimensional motion can be extended to higher dimensional motion as well.
Consider first the case of motion with constant acceleration
such as for example projectile motion. Now I have an equation
such as 
for each dimension:
The conserved quantity analogous to energy in one-dimension
is formed by adding
these equations and multiplying by 
:
The last bracket is a scalar formed from the vectors
and 
. It can be shown that
for arbitrary vectors
where 
is the angle between vectors 
and 
.
Applying this piece of math to Eq. 26 we can write
where the expression for work in higher dimensions becomes
