Moderate -0.8 This is a straightforward linear combination problem requiring students to set up and solve a simple system of two simultaneous equations in two unknowns by equating coefficients. It's routine practice of a standard technique with no conceptual difficulty or problem-solving insight required, making it easier than average.
3 Vectors \(\mathbf { a }\) and \(\mathbf { b }\) are given by \(\mathbf { a } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k }\) and \(\mathbf { b } = 4 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }\).
Find constants \(\lambda\) and \(\mu\) such that \(\lambda \mathbf { a } + \mu \mathbf { b } = 4 \mathbf { j } - 3 \mathbf { k }\).
3 Vectors $\mathbf { a }$ and $\mathbf { b }$ are given by $\mathbf { a } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k }$ and $\mathbf { b } = 4 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$.\\
Find constants $\lambda$ and $\mu$ such that $\lambda \mathbf { a } + \mu \mathbf { b } = 4 \mathbf { j } - 3 \mathbf { k }$.
\hfill \mbox{\textit{OCR MEI C4 2009 Q3 [5]}}