(a)[3]
Write down a vector equation for $l_1$ and determine a vector equation for $l_2$.
(b)[3]
Calculate the acute angle formed by $l_1$ and $l_2$.
(c)[3]
Find the position vector of the point where $l_1$ and $l_2$ intersect.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The line $l_1$ goes through the point $(3, 1, -6)$ and is parallel to the vector $2\mathbf{i} + \mathbf{j} + 4\mathbf{k}$. The line $l_2$ goes through the point $(-1, 3, -6)$ and is perpendicular to the vector $3\mathbf{i} - 2\mathbf{j} + \mathbf{k}$. The direction vector for $l_2$ has no component in the $x$-direction.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Derive $\mathbf r=3\mathbf i+\mathbf j-6\mathbf k+\lambda(2\mathbf i+\mathbf j+4\mathbf k)$” …
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