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

The plane  has vector equation

(a)

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

The plane  has vector equation

where  and  are scalar parameters.

(b)

Show that the vector is perpendicular to 

(c)

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

The plane  has equation

where  and  are scalar parameters.

(a)

Find a Cartesian equation for

The line  has equation

(b)

Find the coordinates of the point of intersection with 

The plane  has equation

(c)

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

where  is a constant

(a)

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

(b)

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

(c)

(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 line  has equation

where  is a scalar parameter.

(a)

Show that and  lie in the same plane.

(b)

Write down a vector equation for the plane containing and 

where  is a constant

(a)

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

(b)

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

(c)

(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.