Vector Problems involving Lines & Planes

Exercises for students:
Solve the following problems and check your working using the above applet:

The equation of the plane p₁ is 8x - z = 6 and the equation of the line l is r = (i + 2j + 3k ) + t(4i + 5j + 6k), where t is a parameter.
Find the position vector of the point of intersection of l and p₁.

The line l has equation r = (i + 2j + 3k ) + t(4i + 5j + 6k) and the plane p has equation r.(2i + 3j - 4k) = 1.
Find the point of intersection of l and p.
Find the acute angle between l and p, correct to the nearest 0.1°.

The equations of the 2 planes P₁ and P₂ are r.(4i + 5j + 6k) = 7 and r.(8i - k) = 6 respectively.
(a) Find the acute angle between the 2 planes, giving your answer to the nearest 0.1°.
(b) Find the length of the projection of the vector 4i + 5j + 6k onto P₂.
(c) Find the equation of the line of intersection of P₁ and P₂, giving your answer in the form r = a + tb.

Right-click here to download a Summary of Vectors.

Right-click here to download a Summary of Vectors with Examples.

Right-click here to download this page and the Java Class File.

Back to H2 Mathematics Homepage