The vectors $a$ and $b$ are shown - HSC - SSCE Mathematics Extension 1 - Question 6 - 2020 - Paper 1
Question 6
The vectors $a$ and $b$ are shown.
Which diagram below shows the vector $v = a - b$?
A.
B.
C.
D.
Worked Solution & Example Answer:The vectors $a$ and $b$ are shown - HSC - SSCE Mathematics Extension 1 - Question 6 - 2020 - Paper 1
Step 1
Identify the Vector Operation
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Answer
In this question, we need to determine the diagram that represents the vector operation v=a−b. This operation indicates that we will subtract vector b from vector a.
Step 2
Visual Representation of the Vectors
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Answer
For the subtraction of vectors, the direction of the second vector (b) is reversed. Therefore, to visualize v=a−b, we draw vector a starting from a point and then from the tip of a, draw vector −b (which is b in the opposite direction).
Step 3
Choosing the Correct Diagram
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Answer
Upon analyzing the diagrams, option D correctly shows vector a, followed by vector −b (in the opposite direction) starting from the tip of vector a to complete the vector v.
