Question

Point \( \mathbf{A} \) and \( \mathbf{B} \) are on the number plane. The vector \( \overrightarrow{A B} \) is \( \left(\begin{array}{l}4 \\ 1\end{array}\right) \). Point \( \mathbf{C} \) is chosen so that the area of triangle \( A B C \) is \( \frac{17}{2} \) square units and \( |\overrightarrow{A C}|=\sqrt{34} \). ii) Find all possible vectors \( \overrightarrow{A C} \). iii) If a point \( M \) divides The vector \( \overrightarrow{A B} \) in the ratio \( 3: 2 \) and a point \( N \) divides The vector \( \overrightarrow{A C} \) In the ratio \( 3: 2 \). Prove that \( \mathrm{MN} \) is parallel to \( \mathrm{BC} \), and find its length in terms of \( \mathrm{BC} \).

          Point \( \mathbf{A} \) and \( \mathbf{B} \) are on the number plane. The vector \( \overrightarrow{A B} \) is \( \left(\begin{array}{l}4 \\ 1\end{array}\right) \).
Point \( \mathbf{C} \) is chosen so that the area of triangle \( A B C \) is \( \frac{17}{2} \) square units and \( |\overrightarrow{A C}|=\sqrt{34} \).
ii) Find all possible vectors \( \overrightarrow{A C} \).
iii) If a point \( M \) divides The vector \( \overrightarrow{A B} \) in the ratio \( 3: 2 \) and a point \( N \) divides The vector \( \overrightarrow{A C} \) In the ratio \( 3: 2 \).
Prove that \( \mathrm{MN} \) is parallel to \( \mathrm{BC} \), and find its length in terms of \( \mathrm{BC} \).

Point 𝐀 and 𝐁 are on the number plane. The vector A B is (
4
1
).
Point 𝐂 is chosen so that the area of triangle A B C is (17)/(2) square units and |A C|=√(34).
ii) Find all possible vectors A C.
iii) If a point M divides The vector A B in the ratio 3: 2 and a point N divides The vector A C In the ratio 3: 2.
Prove that MN is parallel to BC, and find its length in terms of BC.

Added by Lisa B.

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