Hey TimsBobby2.

Remember that your final vector will be v(t) = a_t*a + b_t*b + c_t*c and if (a,b,c) are orthogonal to each other then a_t is the inner product of the function against the vector a that is normalized, with the same for b and c respectively.

First figure out the normalized vectors (if they aren't already normalized) and take the inner product of your function with respect to those vectors.