Vector Problems involving Points & Planes

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

MC N93/II/15 (part)
The point C has position vectors 3i + 4j + 7k respectively, and the plane p has equation r.(3i + j - k) = 6.
Show that the point C lies in the plane p.

MC N93/II/15 (part)
The plane p has equation x + 2y + 3z = 6.
Calculate the coordinates of the point A in p such that the line joining the origin to A is perpendicular to p.

MC J95/II/15 (part)
The plane p has equation r.(2i + j + 2k) = 36.
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.

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