Standard +0.3 This is a standard Further Maths vectors question requiring knowledge that the angle θ between a line (direction d) and plane (normal n) satisfies sin θ = |d·n|/(|d||n|). The calculation is straightforward: dot product gives 2, magnitudes are √2 and √3, leading to sin θ = 2/√6 and θ ≈ 54.7°. Slightly above average difficulty due to being Further Maths content, but it's a routine application of a formula with simple arithmetic.
2.
A plane has equation \(\mathbf { r } \cdot \left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] = 7\)
A line has equation \(\mathbf { r } = \left[ \begin{array} { l } 2 \\ 0 \\ 1 \end{array} \right] + \mu \left[ \begin{array} { l } 1 \\ 0 \\ 1 \end{array} \right]\)
Calculate the acute angle between the line and the plane.
Give your answer to the nearest \(0.1 ^ { \circ }\)
[0pt]
[3 marks]
2.
A plane has equation $\mathbf { r } \cdot \left[ \begin{array} { l } 1 \\ 1 \\ 1 \end{array} \right] = 7$\\
A line has equation $\mathbf { r } = \left[ \begin{array} { l } 2 \\ 0 \\ 1 \end{array} \right] + \mu \left[ \begin{array} { l } 1 \\ 0 \\ 1 \end{array} \right]$\\
Calculate the acute angle between the line and the plane.\\
Give your answer to the nearest $0.1 ^ { \circ }$\\[0pt]
[3 marks]\\
\hfill \mbox{\textit{SPS SPS FM 2020 Q2 [3]}}