Challenging +1.2 This is a Further Maths question requiring students to use three constraints (magnitude, angle with axis, parallel to plane) to find a unique vector. It involves standard techniques (dot product for angle, normal vector for plane condition) but requires careful coordination of multiple conditions and solving a system with a quadratic equation. More challenging than typical A-level questions but still follows established methods without requiring novel insight.
10 A vector \(\mathbf { v }\) has magnitude 1 unit. The angle between \(\mathbf { v }\) and the positive \(z\)-axis is \(60 ^ { \circ }\), and \(\mathbf { v }\) is parallel to the plane \(x - 2 y = 0\).
Given that \(\mathbf { v } = a \mathbf { i } + b \mathbf { j } + c \mathbf { k }\), where \(a , b\) and \(c\) are all positive, find \(\mathbf { v }\).
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10 A vector $\mathbf { v }$ has magnitude 1 unit. The angle between $\mathbf { v }$ and the positive $z$-axis is $60 ^ { \circ }$, and $\mathbf { v }$ is parallel to the plane $x - 2 y = 0$.
Given that $\mathbf { v } = a \mathbf { i } + b \mathbf { j } + c \mathbf { k }$, where $a , b$ and $c$ are all positive, find $\mathbf { v }$.
\section*{END OF QUESTION PAPER}
\hfill \mbox{\textit{OCR MEI Further Pure Core AS 2020 Q10 [7]}}