find the parametric equation of the line of the line through (2,1,0) perpendicular to both <i+j> and <j+k>

Question

I just don't understand what to do with those damn perpendicular vectors... if only they were parallel..

Answer 1

The line equation would be in the form:
(x - 2)/a = (y - 1)/b = z/c, where (a, b, c), or ai + bj + ck, is the direction vector of the line. Since when the vectors are perpendicular to one another, we must have the dot-product of two perpendicular vectors to be zero:
a + b = 0; and b + c = 0.
therefore, a = c = -b. and we may arbitrarily take a = 1 [remember that (a, b, c) is just a direction vector]. The result is:
x - 2 = 1 - y = z