IB Maths AA HL Ahl 3 14 Hl Vector Equations of Lines Questions

Practise forming vector, parametric and Cartesian equations of lines, then using direction vectors for angles, parallelism, intersections and constrained motion.

Exam points

Form vector, parametric and Cartesian equations of 2D or 3D lines from a point and direction vector.
Use direction vectors to calculate angles, parallelism or perpendicularity between lines and interpret the result geometrically.
Apply vector line equations to kinematics, finding positions, times or intersections under stated constraints.

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Study AHL 3.14 (HL)—Vector equations of lines conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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Consider the points A(1,2,3), B(k,-2,1) and C(5,0,2), where $k \in \mathbb{R}$ .

For k=9, let $L_{1}$ be the line passing through A, B and C .

Find a vector equation of the line $L_{1}$ .

attempt to set up a vector equation using a point, a parameter and a direction vector

r=\left(\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right)+\lambda\left(\begin{array}{c} 4 \\ -2 \\ -1 \end{array}\right) \text { (or equivalent) }

Note: " r= " or equivalent must be seen for A1.

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IB Maths AA HL Ahl 3 14 Hl Vector Equations of Lines Questions question 1