Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.10—vector Definitions with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.10—vector Definitions and mirrors Paper 1, 2, 3 style where relevant.
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The point lies on the line segment joining points and such that .
Find the position vector of and its distance from the origin.
A survey drone is monitored from a fixed launch point. Its position relative to the launch point at time seconds is given by . The components represent easting (m), northing (m), and height above the launch point (m).
Determine the speed of the drone.
Calculate the distance of the drone from the launch point when .
Calculate the compass bearing on which the drone is travelling.
A survey drone releases a sensor pod. Its position vector relative to a fixed origin , at time seconds (), is described by , where the -axis is vertical and all distances are in metres.
Demonstrate that the sensor pod moves in a vertical plane and specify an equation of this plane.
Determine a vector expression for the velocity of the sensor pod at time .
By calculating the scalar product, verify that the velocity of the sensor pod is orthogonal to the normal vector of this plane at all times.
Find a vector expression for the acceleration of the sensor pod at time .
Calculate the time when the sensor pod passes the point .
Determine the speed of the sensor pod as it passes this point.
Determine the value of such that and are collinear.
Determine the value of such that and are orthogonal.
Consider the vector .
Calculate the magnitude .
Given the vector , determine the size of the angle .