Year 13 vectors in three dimensions test to download as PDF

This Year 13 vectors in three dimensions test lasts 40 minutes and is marked out of 20. It covers the whole chapter for pupils aged 17-18, and the full answers are on a separate page.

⏱️ Duration : 40 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Working with vectors
\(\mathbf a=3\mathbf i-2\mathbf j+5\mathbf k\) and \(\mathbf b=-\mathbf i+4\mathbf j+2\mathbf k\).
1. Find \(\mathbf a+\mathbf b\). [1 mark]
2. Find \(3\mathbf a-2\mathbf b\). [2 marks]
3. Find \(|\mathbf a|\). [1 mark]
Question 2 – A triangle in three dimensions
The points \(A(2,1,3)\), \(B(5,5,15)\) and \(C(2,1,8)\) are given.
1. Find \(\overrightarrow{AB}\) and show that \(AB=13\). [2 marks]
2. Show that \(AC=5\) and find \(BC\). [1 mark]
3. Find angle \(BAC\). [1 mark]
Question 3 – Collinear points
\(A(1,2,3)\), \(B(3,p,7)\) and \(C(7,11,15)\) are three points that lie on a straight line.
1. Find \(\overrightarrow{AC}\) and use it to find the value of \(p\). [2 marks]
2. Find the ratio \(AB:BC\). [2 marks]
Question 4 – A particle in motion
A particle moves so that its position vector at time \(t\) seconds is \(\mathbf r=(1+3t)\mathbf i+(2-2t)\mathbf j+(4+6t)\mathbf k\) metres.
1. Find the velocity and the speed of the particle. [2 marks]
2. Find the position and the distance from the origin when \(t=5\). [2 marks]
Question 5 – Forces in equilibrium
Three forces \(\mathbf F_1=(2\mathbf i-3\mathbf j+5\mathbf k)\) N, \(\mathbf F_2=(-6\mathbf i+\mathbf j+\mathbf k)\) N and \(\mathbf F_3\) act on a particle of mass 2 kg and the particle is in equilibrium.
1. Find \(\mathbf F_3\) and its magnitude. [2 marks]
2. \(\mathbf F_3\) is removed. Find the acceleration vector and its magnitude. [2 marks]

How to use this Year 13 vectors in three dimensions test

First, revise with the vectors in three dimensions lesson and the worksheet. Then sit the test in one go, with a timer set to 40 minutes. After that, mark your work with the vectors in three dimensions test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Year 13 vectors in three dimensions test as a PDF and print it like a real exam paper. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.