How can I concatenate many Vec<Vec<f64>> to produce another Vec<Vec<f64>>?

Question

Is there an easy and optimal way to combine a and b to get c? I am struggling with this since I can't use index for c because it's not initialized. I am trying to avoid initializing c using 2 vectors of zeroes.

let mut a: Vec<Vec<f64>> = Vec::with_capacity(2);

a.push(vec![1., 2., 3.]);
a.push(vec![4., 5., 6.]);

let mut b: Vec<Vec<f64>> = Vec::with_capacity(2);

b.push(vec![7., 8., 9.]);
b.push(vec![10., 11., 12.]);

let mut c: Vec<Vec<f64>> = Vec::with_capacity(2);

// expected result:
// c: Vec<Vec<f64>> = [[1., 2., 3., 7., 8., 9.], [4., 5., 6., 10., 11., 12.] ]