The vectors $ extbf{a}$ and $ extbf{b}$ are shown - HSC - SSCE Mathematics Extension 1 - Question 6 - 2020 - Paper 1
Question 6
The vectors $ extbf{a}$ and $ extbf{b}$ are shown.
Which diagram below shows the vector $ extbf{v} = extbf{a} - extbf{b}$?
A.
B.
C.
D.
Worked Solution & Example Answer:The vectors $ extbf{a}$ and $ extbf{b}$ are shown - HSC - SSCE Mathematics Extension 1 - Question 6 - 2020 - Paper 1
Step 1
Identify the vector operation: $ extbf{v} = extbf{a} - extbf{b}$
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Answer
To understand the vector extbfv, which is defined as extbfa−extbfb, we need to visualize this operation. Subtracting vector extbfb from vector extbfa can be interpreted as adding the negative of extbfb to extbfa.
Step 2
Visualize $ extbf{b}$ as an opposite vector
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Answer
The negative of vector extbfb, denoted as −extbfb, points in the opposite direction to extbfb. Therefore, to find extbfv, we will draw vector extbfa, followed by vector −extbfb.
Step 3
Combine vectors to find $ extbf{v}$
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Answer
Start at the tip of vector extbfa and draw the vector −extbfb from there. The resultant vector extbfv will point from the tail of extbfa to the tip of −extbfb.
Step 4
Select the correct diagram
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Answer
After visualizing the addition of these two vectors, we can see that the correct diagram illustrating extbfv=extbfa−extbfb is shown in answer option D.
