Practice IB Mathematics Analysis and Approaches (AA) Topic AHL 3.14—vector Equation of Line with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.14—vector Equation of Line and mirrors Paper 1, 2, 3 style where relevant.
Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.
Two lines in three-dimensional space are given by $L_1:\ \mathbf r = \begin{pmatrix} 0\ 1\ 2 \end{pmatrix} +\lambda \begin{pmatrix} 1\ -1\ 2 \end{pmatrix}, \qquad L_2:\ \mathbf r = \begin{pmatrix} 2\ 3\ 0 \end{pmatrix} +\mu
…
The line is given by the parametric equations .
Find the coordinates of the point on that is nearest to the origin.
Two lines are given by $L_1:\ \mathbf r = \begin{pmatrix} 1\ 2\ -1 \end{pmatrix} +\lambda \begin{pmatrix} 2\ -1\ 2 \end{pmatrix}, \qquad L_2:\ \mathbf r = \begin{pmatrix} 5\ -1\ 3 \end{pmatrix} +\mu \begin{pmatrix}
…
(e) Find all points on such that the vector makes an angle of with the direction of , where is the intersection point from part (b). Give exact parameter values and coordinates of if they exist.
(e) Find the minimum distance between the objects.
Two lines in three-dimensional space are given by
(a) Write both lines in parametric and Cartesian form.
(b) whether the lines are skew, parallel, coincident, or intersecting. If they intersect, find the point of intersection.
(c) Find the acute angle between and , giving exact values for and .
(d) Let . Find the shortest distance from to the line , and the coordinates of the foot of the perpendicular from to .
In this question, distances are in km and times in hours.
Object passes through point at time with constant velocity . Object passes through point at time with constant velocity .
(a) Find the speed of each object.
(b) Write down the position vector of:
(i) object at time ;
(ii) object at time .
(c) Show that the two objects do not collide.
(d) Find the time at which the two objects are closest.
