Same length, different vectors
Same length, different vectors
Secondary 4
4 marks
It is given that \(\overrightarrow{EF}=\begin{pmatrix}6\\ -8\end{pmatrix}\) and \(\overrightarrow{GH}=\begin{pmatrix}-8\\ -6\end{pmatrix}\).
- Write down \(\overrightarrow{FE}\) as a column vector.[1]
- A student says that \(\overrightarrow{EF}=\overrightarrow{GH}\) because the two vectors have the same length. Work out both lengths and say whether the student is right, giving a reason.[3]
Solution:
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Answer:(a) \(\overrightarrow{FE}=\begin{pmatrix}-6\\ 8\end{pmatrix}\) (b) Both lengths are 10; the student is wrong: the directions differ, since \(6\neq-8\), so the vectors are not equal
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