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 $ar{AB} + ar{CQ}$?
A. $ar{AQ}$
B. $ar{CP}$
C. $ar{PB}$
D. ... show full transcript
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
Identify the components of the vectors
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Answer
To solve the problem, we start by identifying the vectors in the equation ar{AB} + ar{CQ}. The segments ar{AB} and ar{CQ} connect points A and B, and C and Q, respectively. We assign each vector a representation based on their defined endpoints in the diagram.
Step 2
Express each vector in terms of known segments
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Answer
The vector ar{AB} can be expressed as the distance from point A to point B, while ar{CQ} represents the distance from point C to point Q. Knowing the layout of the cubes, we can examine the relationships. In particular, based on the arrangement, ar{CQ} translates through the sequence of cubes to reach point Q.
Step 3
Combine the vectors
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Answer
Combining these vectors, we analyze the resultant position of point Q in relation to A through the bridge defined by segments in the cubes. By simplifying our expression, we derive how ar{AB} and ar{CQ} relate to other options presented in the choices.
Step 4
Select the correct answer
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Answer
After considering the vector additions, we see that the sum corresponds to ar{CP}, which directly connects points C and P in the layout. Thus, the correct answer is B. ar{CP}.
