The plane P1 passes through the P, with position vector i + 2j – k, and is perpendicular to the line L with equation
r = 3i – 2k +l(-i + 2j + 3k)
They got the normal to the plane to be : – i + 5j + 3k
How did they get that? Thanks in advance.
(Sorry for the strange font, I can't be bothered to edit the font.)
So a line in the form:
where 'a' is position vector and 'b' is direction vector. If this is perpendicular to a plane, does that always mean that the 'n' for the plane is 'b'.
So r.n=a.n < Equation of plane. n is normal which the direction vector of a perpendicular line.
Is that correct?
Another Question:
The Points A, B and C lie on the plane P and, relative to a fixed origin O, they have position vectors
a = 3i - j + 4k, b = -i + 2j, c = 5i - 3j + 7k
Find an equation of Pin the form r.n = p.
^ I worked out direction vector of AB and AC but how do I work out n?