From the above figure, which of the following is incorrect?

Question

From the above figure, which of the following is incorrect?

BlackTom AI · Accepted Answer

Examining the figure, we need to assess the relationships between the labeled vectors a, b, x, y, w, u, v, and z along the grid.
Option 1: y = (3/4) z. Here y and z are both horizontal arrows on the right side of the diagram, but y is drawn shorter than z. If the scale on the grid is consistent, the ratio of their lengths appears plausible to be 3:4, making y a 3/4 length of z. This would be a reasonable proportional relationship given their visual sizes, so this statement could be true.
Option 2: z = -(4/5) w. Both z and w point to the right (same direction), with z noticeably shorter than w. Since the arrow directions are the same, the negative sign would imply opposite directions, which is not the case in the diagram. Therefore this relation is incorrect because it asserts opposite directions between z and w, contrary to what is shown.
Option 3: x = y. The arrows x and y lie on the same horizontal line family but at different vertical positions; x appears longer than y in the diagram. If they are drawn with different lengths, the equality x = y would be false. However, depending on the exact scale drawn, some tests might interpret them as potentially equal, but visually they do not appear identical in length, so this is likely false.
Option 4: u = v. Vectors u and v are shown as two distinct diagonal arrows in the lower-middle region of the figure, pointing in different directions and with different magnitudes. They are not the same vector, so the statement u = v is not true. This is a clear mismatch if one reads the diagram carefully.

In summary, each option requires comparing lengths and directions from the diagram:
- The claim y = (3/4) z aligns with a proportional, same-direction relationship consistent with their drawn lengths, so it is plausible as true.
- The claim z = -(4/5) w asserts opposite directions between z and w, which contradicts the diagram where both point right; thus it is incorrect.
- The claim x = y asserts equal lengths for two clearly different horizontal arrows; this is unlikely and typically false.
- The claim u = v asserts identical vectors, which the diagram shows as distinct in both direction and magnitude; thus it is false.

Therefore, the options that are incorrect are the ones that claim opposite direction for z and w (Option 2) and those asserting equality of lengths or vectors that are drawn differently (Options 3 and 4). The reasoning above explains the specific visual cues that support or contradict each statement.

SMAT011 Week 1 Practice Quiz

From the above figure, which of the following is incorrect?

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