Further Maths further vectors test to download as PDF

This Further Maths further vectors test lasts 60 minutes and is marked out of 20. It covers the whole chapter for pupils aged 16-18, and the full answers are on a separate page.

⏱️ Duration : 60 min
🎯 Total : 20 marks
❓ 5 questions

Mark/20

Question 1 – Scalar and vector products
The vectors are \(\mathbf a=\mathbf i+2\mathbf j-\mathbf k\) and \(\mathbf b=3\mathbf i+2\mathbf k\).
1. Find the angle between \(\mathbf a\) and \(\mathbf b\) to 1 decimal place. [3]
2. Find \(\mathbf a\times\mathbf b\) and the area of the triangle with sides \(\mathbf a\) and \(\mathbf b\). [2]
Question 2 – Line and plane
The line \(l\) is \(\mathbf r=(2,-1,0)+\lambda(1,2,-2)\) and the plane \(\Pi\) is \(3x+y-z=7\).
1. Find the coordinates of the point where \(l\) meets \(\Pi\). [3]
2. Find the acute angle between \(l\) and \(\Pi\) to 1 decimal place. [2]
Question 3 – Equation of a plane
The points are \(A(1,1,1)\), \(B(2,0,3)\) and \(C(0,2,2)\).
1. Find \(\overrightarrow{AB}\times\overrightarrow{AC}\) and hence the Cartesian equation of the plane \(ABC\). [3]
2. Find the distance from \(D(3,3,3)\) to the plane. [1]
Question 4 – Distance from a point to a line
Find the shortest distance from \(P(1,4,2)\) to the line \(\mathbf r=(0,1,0)+\lambda(1,1,2)\). [3]
Question 5 – Problem: the solar panel
A solar panel lies in the plane \(3x+4z=12\), where \(z\) is vertical and distances are in metres. Sunlight arrives in the direction \(-\mathbf i-2\mathbf k\).
1. Find the angle between the panel and the horizontal. [1]
2. Find the angle between the sunlight and the panel. [2]

How to use this Further Maths further vectors test

First, revise with the further vectors lesson and the worksheet. Then sit the test in one go, with a timer set to 60 minutes. After that, mark your work with the further vectors test answers. If you lose marks on a question, redo it the next day without help.

Finally, you can download this Further Maths further vectors 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.