If two forces P and Q are such that |P + Q| = |P - Q|, then the angle between P and Q is:
Correct answer: C. 90 degree
- A. 0 degree
- B. 30 degree
- C. 90 degree
- D. 180 degree
Explanation
To solve this problem, use the properties of vector addition and subtraction. When |P + Q| = |P - Q|, the vectors P and Q must be perpendicular to each other. This occurs when the angle between them is 90 degrees.In terms of vector mathematics, this situation implies:P^2 + Q^2 + 2PQcos(x) = P^2 + Q^2 - 2PQcos(x)Solving this for x gives 4PQcos(x) = 0, which simplifies to cos(x) = 0. Therefore, x = 90 degrees.Options 0 degrees and 180 degrees would result in the magnitudes being clearly unequal due to vector alignment or opposition, respectively. Option 30 degrees would also not satisfy the condition of equal magnitudes.
This question appeared on the ETEA MDCAT 2012 paper, which you can sit online with every answer explained.
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About Addition of Vectors
Vector addition combines directed quantities using the head-to-tail, parallelogram and component methods. Work includes finding the resultant magnitude and direction for two or more vectors, resolving vectors into perpendicular components, and distinguishing vector addition from scalar addition, where direction has no role.
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