Mathematics 1229A/B Lecture Notes - Lecture 5: Cross Product, Dot Product

• School: Western University
• Department: Mathematics
• Course: Mathematics 1229A/B
• Professor: Kuzmin

Document Summary

Math 1229 lecture 5 lines and planes. Two-point form for a line in r2 through points p(x1,y1) and q(x2,y2) is (x,y) = (1 - t)(x1,y1) + t(x2,y2). In r3 through points p(x1,y1z1) and q(x2,y2,z2) is (x,y,z) = (1 t)(x1,y1,z1) + t(x2,y2,z2) Find two-point form of the line through points (1,7,-3) and (4,0,2). (x,y,z) = (1 t)(1,7,-3) + t(4,0,2) Definition: a normal to a plane is a vector n that is perpendicular to every vector in the plane. An equation of the plane through point p(xo,yo,zo) with normal n = (a,b,c), which is given by ax + by + cz = d which is called standard form. Find an equation in standard form of the plane through point (4,-1,3) with normal n = (3,5,2) Standard form: 3x + 5y + 2z = d. Find an equation in standard form of the plane through points p(2,1,3), q(4,2,-1) and. Note find the cross product for perpendicular vectors.