Find the standard matrix of an orthogonal projection

Problem 4. Let W = Span[w1; w2], where

w1 = [3 0 4]

w2 = [4 5 -3]

If T (from R^3 to R^3) is the orthogonal projection onto W, find the standard matrix of T.

I did this by finding the orthogonal projections of e1, e2, and e3 on span W and constructing the transformation from [e1 e2 e3]

My answer was :

0.680 0.400 0.240

0.400 0.500 -0.300

0.240 -0.300 0.820

Is this correct? I double checked by finding that the applying the transformation matrix to w1 and w2 returned w1 and w2 which is what it should do. Thanks!