a) Give parametric equation (point-direction form) of the line which lies on both of the planes:
x + y + z = 1 and d x + 2y + 10z = 2. What is the direction d of this line?
b) Let n1 and n2 be the normal vectors to the two given planes. Without actual computation,
describe the relationship between d and n1 × n2.
a) if Ax + Bx +Cz =D is the equation of a plane , then the vector normal to the given plane is
Equation of f2 is
Therefore the normal vector
b) We have and
Then and are perpendicular to the line of intersection. Therefore is the perpendicular to both and and hence parallel to the plane line of intersection
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