Vector Planes (Edexcel A Level Further Maths: Core Pure): Exam Questions

where  is a constant

Find the values of for which the matrix  has an inverse.

Find, in terms of , the coordinates of the point where the following planes intersect

(i) Find the value of for which the set of simultaneous equations

can be solved.

(ii) For this value of , interpret the solution of the set of simultaneous equations geometrically.

where  is a constant

Given that find, in terms of , the inverse of the matrix .

Find, in terms of, the coordinates of the point where the following planes intersect.

(i) Find the value of for which the following planes intersect in a straight line.

(ii) For this value of , determine a vector equation for the line of intersection.

The line has equation 

The plane  has equation 

The line  is the reflection of the line in the plane

Find a vector equation of the line 

The plane  has vector equation

Find the perpendicular distance from the point (6, 2, 12) to the plane

The plane  has vector equation

where  and  are scalar parameters.

Show that the vector is perpendicular to 

Show that the acute angle between and is 52° to the nearest degree.

The plane  has equation

where  and  are scalar parameters.

Find a Cartesian equation for

The line  has equation

Find the coordinates of the point of intersection with 

The plane  has equation

Find, to the nearest degree, the acute angle between  and