(a) Prove that the vectors form an orthogonal basis of R3 with the dot product. (b) Use...

Question:

(a) Prove that the vectors

form an orthogonal basis of R3 with the dot product.
(b) Use orthogonality to write the vector v = (1, 2, 3)T as a linear combination of v1, v2, v3.
(c) Verify the formula (5.8) for ||v||.
(d) Construct an orthonormal basis, using the given vectors.
(e) Write v as a linear combination of the orthonormal basis, and verify (5.5).