Solve the problem.Show that the vectors 
b + 
a and 
b - 
a are orthogonal.
What will be an ideal response?
Take the dot product:
(
b + 
a) ? (
b - 
a) = (
b + 
a) ? 
b - (
b + 
a) ? 
a
= (
b) ? (
b) + (
a) ? (
b) - (
b) ? (
a) - (
a) ? (
a)
= 
2b?b + 
a ? b - 
a ? b - 
2 a?a
= 
2 
2 - 
2 
2 = 0
Since the dot product is zero and since neither vector is identically zero, then the vectors are orthogonal.
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