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Quick questions on Further vectors: lines, planes, scalar and vector products - Edexcel A-Level Further Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is line-plane angle?
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The dot product of direction and normal gives the angle to the normal, so use sin⁑\sin in the line-plane formula, or subtract from 90∘90^\circ.
What is sign slips in the cross product?
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The middle component of aΓ—b\mathbf{a}\times\mathbf{b} is a3b1βˆ’a1b3a_3 b_1 - a_1 b_3 (note the reversed order); writing a1b3βˆ’a3b1a_1 b_3 - a_3 b_1 flips the sign of the whole result.
What is q1?
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Find a normal to the plane through a=(100)\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} containing directions (110)\begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix} and (011)\begin{pmatrix} 0 \\ 1 \\ 1 \end{pmatrix}. [3 marks]
What is q2?
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Are the vectors (21βˆ’1)\begin{pmatrix} 2 \\ 1 \\ -1 \end{pmatrix} and (1βˆ’11)\begin{pmatrix} 1 \\ -1 \\ 1 \end{pmatrix} perpendicular? [2 marks]
What is q3?
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Find the point where the line r=(000)+Ξ»(111)\mathbf{r} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} + \lambda\begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} meets the plane x+y+z=6x + y + z = 6. [3 marks]

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