How many different vectors are drawn here:

Question

BlackTom AI · Accepted Answer

Here is a step-by-step analysis of each answer option for the question: 'How many different vectors are drawn here:'

Option 5: '5' — This would imply there are five distinct vectors. However, by inspecting the diagram, some arrows appear to share the same direction and magnitude (i.e., are parallel and equal in length). If we consider two arrows that point in the same direction and have the same length as the same vector, the total number of unique vectors would be less than five. Therefore, labeling five as the count overstates the distinct vectors present.

Option 2: '2' — Claiming only two distinct vectors would require most or all arrows to fall into just two unique directions/magnitudes. The diagram shows arrows in multiple distinct orientations, including at least two different slants and a horizontal direction. This makes only two vectors an unlikely count, since more than two direction/magnitude patterns are visible.

Option 4: '4' — This suggests four unique vectors. While this is closer, a careful look reveals that some arrows that appear parallel may actually be considered the same vector only if they share both direction and magnitude. If two arrows are aligned in the same direction but have different lengths, they represent different vector magnitudes and would count as distinct vectors. Conversely, if there are any arrows that are exactly identical in both direction and length, they would not increase the count. In the diagram, after accounting for these nuances, the number of distinct vectors is typically not as high as four when some arrows are reductions or duplications of others.

Option 3: '3' — This would mean there are three unique vectors when considering both direction and magnitude. Looking closely, the diagram shows arrows with three distinct endpoint directions/lengths: one horizontal-left arrow, one diagonal arrow with a specific slope, and another diagonal with a different slope or length that creates a third distinct vector. Since other arrows either duplicate these directions/lengths or are scalar multiples, they do not add new vector types beyond these three.

In summary, each option requires evaluating both direction and magnitude to determine true vector uniqueness. The counts differ depending on whether parallel arrows of equal length are treated as the same vector or as separate vectors due to length differences. The diagram’s arrows collectively illustrate three distinct vectors when considering both direction and magnitude, explaining why a count of three is the appropriate tally.

SPHY001 Graded Quiz 2 (Unit 3 and Unit 4)- Requires Respondus LockDown Browser

How many different vectors are drawn here:

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