- Use the equation of a plane in any of the forms ax + by + cz = d or r.n = p
or r = a + λb + μc and convert equations of planes from one form to another as necessary in solving problems - Recall that the vector product a × b of two vectors can be expressed either as absinθn ̂ ,where n ̂ is a unit vector, or in component form ai+bj+ck
- Use equations of lines and planes, together with scalar and vector products where appropriate, to solve problems concerning distances, angles and intersections, including
– determining whether a line lies in a plane, is parallel to a plane or intersects a plane, and finding the point of intersection of a line and a plane when it exists
– finding the foot of the perpendicular from a point to a plane
– finding the angle between a line and a plane, and the angle between two planes
– finding an equation for the line of intersection of two planes
– calculating the shortest distance between two skew lines
– finding an equation for the common perpendicular to two skew lines.
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