Mathematics 1229A Assignment 1 Due by 12 noon EDT on Wednesday June 1, 2016 Reminder: Except for the True/False questions, you must show sufficient...

Consider the line ℓ1, which passes through P(5, 0, 4) and is parallel to ~u = (2, 1, 3), and

the line ℓ2, which passes through Q(0, 2, 1) and is parallel to ~v = (1,−1, 0). Let R be the

point at which ℓ1 and ℓ2 intersect.

(a) Vector ~n is perpendicular to both

−→

PR and

−→

QR, and has first component 1. (i.e.

~n = (1, a, b) for some numbers a and b.) Without finding point R, find vector ~n.