Solve the problem.Show that the vectors b + a and b - a are orthogonal.

Question

What will be an ideal response?

Answer 1

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.