In the above figure, how many pairs of equal vectors are there?

Question

In the above figure, how many pairs of equal vectors are there?

BlackTom AI · Accepted Answer

First, I will restate the problem and all answer choices to set the scene. The question asks: In the above figure, how many pairs of equal vectors are there? The options are: 2, 3, 1, 0.

Now I’ll analyze each option one by one, looking for vectors that have both the same magnitude and the same direction, since that is what makes two vectors equal.

- Option 2 (two pairs): To have two pairs of equal vectors, we would need at least four vectors forming two distinct equal-length, same-direction pairs. In the diagram, there appear to be several horizontal rightward arrows of different lengths, and a mix of other directions. If only two arrows share a length and direction, you would only get one equal pair, not two distinct pairs. Therefore, this option seems unlikely unless there are two separate identical-length, identical-direction groups.

- Option 3 (three pairs): Three pairs would require at least six vectors arranged into three separate equal-length, same-direction groups. The layout shown does not support such a large number of identical vectors sharing both magnitude and direction; the horizontal arrows vary in length and there aren’t multiple complete groups of the same length and direction. Thus this option is unlikely.

- Option 1 (one pair): If exactly one pair of vectors shares both magnitude and direction with another vector in the figure, that would yield a single equal pair. Visually, I can imagine two of the horizontal arrows that look to be the same short length and both pointing to the right. If that is the case, there is exactly one pair of equal vectors corresponding to those two arrows.

- Option 0 (no pairs): Saying there are zero equal pairs would require all vectors to have unique lengths or directions. Given the presence of at least two horizontal arrows that appear to be the same short length and same direction, this option would contradict the diagram’s evident symmetry in that subset. So this is unlikely.

Putting the observations together, the most plausible count that fits the diagram is exactly one pair of equal vectors, corresponding to the two arrows that share the same short length and direction.

SMAT011 Week 1 Practice Quiz

In the above figure, how many pairs of equal vectors are there?

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