If A and B are two vectors, then the correct statement is:
Correct answer: A. A + B = B + A
- A. A + B = B + A
- B. A - B = B - A
- C. A x B=B x A
- D. None of the above
Explanation
(a) A + B = B + A: This statement represents the commutative property of vector addition, which means that the order in which we add two vectors does not affect the result. So, adding vector A to vector B is the same as adding vector B to vector A. (b) A - B = B - A: This statement is incorrect. The subtraction of vectors is not commutative. If you subtract vector B from vector A, it is not the same as subtracting vector A from vector B. The order matters in vector subtraction. (c) A x B = B x A: This statement represents the commutative property of vector cross product. However, the cross product is a vector operation, not an addition or subtraction operation. So, this option is not relevant to the given question. (d) None of the above: This option is incorrect because the correct statement is (a) A + B = B + A.
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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