Four cubes are placed in a line as shown on the diagram - HSC - SSCE Mathematics Extension 2 - Question 1 - 2021 - Paper 1
Question 1
Four cubes are placed in a line as shown on the diagram.
Which of the following vectors is equal to $oldsymbol{AB + CQ}$?
A. $oldsymbol{AQ}$
B. $oldsymbol{CP}$
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Worked Solution & Example Answer:Four cubes are placed in a line as shown on the diagram - HSC - SSCE Mathematics Extension 2 - Question 1 - 2021 - Paper 1
Step 1
Determine the components of $AB$
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Answer
The vector AB represents the movement from point A to point B. In the context of the cubes, this represents one unit in the direction of the cubes.
Step 2
Determine the components of $CQ$
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Answer
The vector CQ moves from point C to point Q. Each cube is adjacent to the next, so CQ is equivalent to moving up to two whole cubes plus the segment from C to D, contributing another unit distance.
Step 3
$oldsymbol{AB+CQ}$
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Answer
Combining both vectors gives:
AB+CQ=1+2=3
This means we are looking for a vector that has a total movement over three units.
Step 4
Evaluate the options
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Answer
Comparing each option:
A: AQ — This is not valid as it does not represent the combination.
B: CP — This is correct as it spans the units required to match AB+CQ.
C: PB — This does not encompass the required distance.
D: RA — This does not match either.
Thus, the correct answer is B.
