What is the angle between(P+Q) and(P×Q)
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The Answer is 90 degree. Let me elaborate it. Assume a and b to be two sides of a parallelogram as shown in figure.
AB|=a and |BC|=b; We have AB+BC+CD+DA=0 ;|AB|=|CD|; AB=-CD; BC= -DA . AB +BC represent the diagonal vector BD ->AB+BC = BD and AB + AD represent diagonal AC -> AB+DA=AC which implies AB -BC = AC .BD and AC are perpendicular .Thus,AB+BC is perpendicular to AB-BC
AB|=a and |BC|=b; We have AB+BC+CD+DA=0 ;|AB|=|CD|; AB=-CD; BC= -DA . AB +BC represent the diagonal vector BD ->AB+BC = BD and AB + AD represent diagonal AC -> AB+DA=AC which implies AB -BC = AC .BD and AC are perpendicular .Thus,AB+BC is perpendicular to AB-BC
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