Maria starts at the origin and walks along all of the vector $2 extbf{i} + 3 extbf{j}$, then walks along all of the vector $3 extbf{i} - 2 extbf{j}$ and finally along all of the vector $4 extbf{i} - 3 extbf{j}$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2020 - Paper 1
Question 4
Maria starts at the origin and walks along all of the vector $2 extbf{i} + 3 extbf{j}$, then walks along all of the vector $3 extbf{i} - 2 extbf{j}$ and finally alon... show full transcript
Worked Solution & Example Answer:Maria starts at the origin and walks along all of the vector $2 extbf{i} + 3 extbf{j}$, then walks along all of the vector $3 extbf{i} - 2 extbf{j}$ and finally along all of the vector $4 extbf{i} - 3 extbf{j}$ - HSC - SSCE Mathematics Extension 1 - Question 4 - 2020 - Paper 1
Step 1
Walks along the vector $2i + 3j$
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Answer
Starting from the origin (0, 0), the position after walking the vector 2extbfi+3extbfj becomes:
(0+2,0+3)=(2,3).
Step 2
Walks along the vector $3i - 2j$
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Answer
Now from the position (2, 3), walking along the vector 3extbfi−2extbfj:
(2+3,3−2)=(5,1).
Step 3
Walks along the vector $4i - 3j$
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Answer
Finally, from the position (5, 1), walking along the vector 4extbfi−3extbfj:
(5+4,1−3)=(9,−2).
Step 4
Calculate the distance from the origin
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Answer
The final coordinates are (9, -2). To find the distance from the origin, we use the distance formula:
