OCR MEI C4 — Question 2 5 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeLinear combination of vectors
DifficultyModerate -0.8 This is a straightforward linear combination problem requiring students to set up and solve a system of three simultaneous equations by equating coefficients of i, j, and k. The method is standard and mechanical with no conceptual challenges—easier than average for A-level.
Spec1.10d Vector operations: addition and scalar multiplication
2 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 \(\lambda \mathbf { a } + \mu \mathbf { b } = 4 \mathbf { j } - 3 \mathbf { k }\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(4\mathbf{j} - 3\mathbf{k} = \lambda\mathbf{a} + \mu\mathbf{b}\)
\(= \lambda(2\mathbf{i} + \mathbf{j} - \mathbf{k}) + \mu(4\mathbf{i} - 2\mathbf{j} + \mathbf{k})\)M1
\(0 = 2\lambda + 4\mu\)M1 equating components
\(4 = \lambda - 2\mu\)A1 at least two correct equations
\(-3 = -\lambda + \mu\)
\(\lambda = -2\mu,\ 2\lambda = 4 \Rightarrow \lambda = 2,\ \mu = -1\)A1, A1 [5] 
## Question 2:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $4\mathbf{j} - 3\mathbf{k} = \lambda\mathbf{a} + \mu\mathbf{b}$ | | |
| $= \lambda(2\mathbf{i} + \mathbf{j} - \mathbf{k}) + \mu(4\mathbf{i} - 2\mathbf{j} + \mathbf{k})$ | M1 | |
| $0 = 2\lambda + 4\mu$ | M1 | equating components |
| $4 = \lambda - 2\mu$ | A1 | at least two correct equations |
| $-3 = -\lambda + \mu$ | | |
| $\lambda = -2\mu,\ 2\lambda = 4 \Rightarrow \lambda = 2,\ \mu = -1$ | A1, A1 [5] | |

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2 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  Q2 [5]}}
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Q1 6 Q2 5 Q3 6