(i)[6]
Determine the equation of plane $BCD$, and present it in the form $ax + by + cz = d$.
(ii)[4]
Calculate the acute angle between planes $BCD$ and $OABC$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The diagram displays rectangular axes $Ox$, $Oy$ and $Oz$, together with four points $A$, $B$, $C$ and $D$, whose position vectors are $\overrightarrow{OA} = 3\mathbf{i}$, $\overrightarrow{OB} = 3\mathbf{i} + 4\mathbf{j}$, $\overrightarrow{OC} = \mathbf{i} + 3\mathbf{j}$ and $\overrightarrow{OD} = 2\mathbf{i} + 3\mathbf{j} + 5\mathbf{k}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Produce a vector parallel to the plane, such as $\overrightarrow{CB}=2\mathbf{i}+\mathbf{j}$” …
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