AQA A Level Further Maths
Topic questions Pure mathematics Vector equation of a line
8 questions · 79 marks · about 1.5 hours
Show that the angle between L1 and L2 is 0.701 radians, correct to three decimal places.
Find the shortest distance between L1 and L2
Give your answer in an exact form.
The line l1 passes through the points A(6, 2, 7) and B(4, 
3, 7)
Find a Cartesian equation of l1
Explain how you know that the lines l1 and l2 are not perpendicular.
The lines l1 and l2 both lie in the same plane.
Find the value of c
In this question all measurements are in centimetres.
A small, thin laser pen is set up with one end at A(7, 2, 
3) and the other end at
A laser beam travels from A to B and continues in a straight line towards a large thin sheet of glass.
The sheet of glass lies within a plane 
1 which is modelled by the equation
where p is an integer.
A second large sheet of glass lies on the other side of 
1
This second sheet lies within a plane 
2 which is modelled by the equation
Calculate the distance between the sheets of glass.
The point A(7, 2, 3) is reflected in 1
Find the coordinates of the image of A after reflection in 1
Find the acute angle between the lines L1 and L2, giving your answer to the
Find the equation of 1, giving your answer in the form r.n 
d
Hence find the shortest distance of the plane 1 from the origin.
The Cartesian equation of the line L1 is
The Cartesian equation of the line L2 is
Calculate the values of the constants b, c, m and p
Fully justify your answers.
Explain how you know that two of the lines are parallel.
Show that the perpendicular distance between these two parallel lines is 7.95 units, correct to three significant figures.
Show that the lines l1 and l3 meet, and find the coordinates of their point of intersection.
The points A(5, 
4, 6) and B(6, 6, 8) lie on the line L. The point C is (15, 
5, 9).
D is the point on L that is closest to C.
Find the coordinates of D.
Hence find, in exact form, the shortest distance from C to L.
The line L1 has equation
The line L2 has equation
Find the shortest distance between the two lines, giving your answer to three significant figures.
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