Standard +0.3 This is a straightforward vector combination problem requiring students to set up and solve simultaneous equations (3 equations, 2 unknowns) to find λ and μ, then state that the four points are coplanar. The algebraic manipulation is routine for C4 level, and the geometric interpretation is a standard result. Slightly easier than average due to its predictable structure and direct application of taught methods.
The points A, B and C have coordinates \(A(3, 2, -1)\), \(B(-1, 1, 2)\) and \(C(10, 5, -5)\), relative to the origin O.
Show that \(\overrightarrow{OC}\) can be written in the form \(\lambda\overrightarrow{OA} + \mu\overrightarrow{OB}\), where \(\lambda\) and \(\mu\) are to be determined.
What can you deduce about the points O, A, B and C from the fact that \(\overrightarrow{OC}\) can be expressed as a combination of \(\overrightarrow{OA}\) and \(\overrightarrow{OB}\)? [6]
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The points A, B and C have coordinates $A(3, 2, -1)$, $B(-1, 1, 2)$ and $C(10, 5, -5)$, relative to the origin O.
Show that $\overrightarrow{OC}$ can be written in the form $\lambda\overrightarrow{OA} + \mu\overrightarrow{OB}$, where $\lambda$ and $\mu$ are to be determined.
What can you deduce about the points O, A, B and C from the fact that $\overrightarrow{OC}$ can be expressed as a combination of $\overrightarrow{OA}$ and $\overrightarrow{OB}$? [6]
\hfill \mbox{\textit{OCR MEI C4 2013 Q5 [6]}}