Vector product

Find a vector that is normal to the plane ∏ 5 (a)

Find a Cartesian equation of the plane ∏ 5 (b)

The position vectors of the points A, B and C are

respectively.

Find the area of the triangle ABC

The points A, B and C all lie in the plane

Find an equation of the plane , in the form r n d

The point P has position vector p i 4j 2k

Find the exact distance of P from

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.

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, B and C have coordinates A(4, 5, 2), B(3, 2, 4) and C(2, 6, 1)

The points A, B and C lie in a plane.

Find a vector equation of the plane in the form r.n k

Hence find the exact distance of the plane from the origin.

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.