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. $ar{PB}$... 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 required vector: $ar{AB} + ar{CQ}$
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Answer
To find the vector ar{AB} + ar{CQ}, we first note the positions of the points A, B, C, and Q in relation to each other.
Step 2
Calculating the components
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Answer
The vector ar{AB} can be expressed as:
ar{AB} = ar{A} + ar{B}
The vector ar{CQ} is calculated using the positions defined in the diagram. We recognize that Q is 3 units away from C along the line. Therefore:
ar{CQ} = ar{C} + 3( ext{direction from C to Q})
Step 3
Combine the vectors
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After simplifying, we need to determine which option matches this resultant vector. The diagram indicates that the position vector from C to P and A to Q can provide a relationship that can help us conclude:
Step 4
Choose the correct option
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Answer
Upon evaluating the choices:
A. ar{AQ} does not represent the same sum.
B. ar{CP} correctly represents the addition we calculated as it bisects the points.
C. ar{PB} is incorrect as it is not representing the vector sum.
