Vector Problems involving Points & Planes
Exercises for students:
Solve the following problems and check your working using the above applet:
The plane p has equation r.(8i - k) = 6.
Show that the point A(1, -1, 2) lies in the plane p.
Show that the point B(1, -1, 3) does not lie in the plane p.
The plane p has equation x + 2y + 2z = 6.
Calculate the coordinates of the point N in p such that the line joining the origin to N is perpendicular to p.
Find the position vector of the foot of the perpendicular from the point A(3, 3, 3) to p.
The plane p has equation r.(2i + j + 2k) = 3.
Find the perpendicular distance from the origin O to p.
The point B has position vector i + 3j + 2k. Find the perpendicular distance from B to p.
The planes p1 and p2 have equations 2x + 3y + 6z = -1 and 2x + 3y + 6z = 6 respectively.
Find the distance between the 2 planes.
The planes p1 and p2 have equations 2x + 8y + 16z = 4 and -x - 4y - 8z = 7 respectively.
Show that the 2 planes are parallel and find the distance between them.
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.
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