Vector A in the drawing is equal to

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BlackTom AI · Accepted Answer

Let’s break down what each labeled vector represents and how vector addition works in this diagram.
Option 1: C + D + E. If we add these three vectors tip-to-tail, the resultant would depend on magnitudes and directions of C, D, and E. However, visually summing C (down-right), D (up-right), and E (left) does not align with the horizontal rightward direction of A, so this combination is unlikely to produce A. The directions largely cancel out components, making it inconsistent with A’s single-rightward direction.
Option 2: C + D. Adding C (down-right) and D (up-right) yields a resultant vector that points to the right, but its vertical components cancel if D is steeper than C, leaving a shorter or differently oriented vector than A. Since A appears as a distinct rightward vector, this two-vector sum does not match A exactly.
Option 3: B + F. B is vertical up, F is down-left (opposite/angled). Summing these tends to produce a resultant that has a significant vertical component or a leftward component, not a clean rightward A. Therefore this combination does not align with A.
Option 4: B + C. Here, B is straight up and C is down-right. When you add B (up) to C (down-right), the vertical components can cancel partially, leaving a net rightward component that aligns with A’s horizontal rightward direction. The resulting vector often points to the right with appropriate magnitude, matching A as drawn. This makes B + C a plausible decomposition of A.
In summary, among the given combinations, only B + C yields a resultant vector directed to the right in the same line as A, consistent with vector addition rules and the diagram’s geometry. The other sums produce vectors with vertical components or leftward components that do not coincide with A’s orientation.

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Vector A in the drawing is equal to

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