What is the Symmetric Matrix Associated with a Quadratic Form in R3?

[Locoism]

Homework Statement

Consider the quadratic form
q(v) = x₁² + 5x₂² + 11x₃² + 4x₁x₂ + 6x₁x₃ + 14x₂₃

Relative to the standard basis of R3 find the symmetric matrix A associated with q.

The Attempt at a Solution

In the standard basis, I'll use
e₁ = [1,0,0]
e₂ = [0,1,0]
e₃ = [0,0,1]

if it were in R2, I would say [a_ij] = q(e_i,e_j) but how do I do this in R3? and I only have 3 variables, so I have to only use one vector, but which entry in the matrix does each one represent?
How do I determine which vectors to use for with entries.

*edit* I'll just specify, if I wanted to find [a₁₁] I could just use q(e₁), but what about [a₂₁] for example?

 

[Locoism]

my book does not explain anything... Can anyone recommend a good one?