A vector equation for a given straight line is r = (i + 3j) + lambda (-i - j)

Question

Construct a vector equation for the line that does go through the point (1,2), and is perpendicular to r.

and

Determine the point of intersection of the two lines

Answer 1

you know that i-j is perpendicular to -i-j since (-1)(1) + (-1)(-1) = -1+1 = 0

so, i+2j + alpha(i - j) will do the trick

1-lambda = 1 + alpha
3-lambda = 2 - alpha

intersect where lambda = 1/2 alpha = -1/2, at the point (1/2,5/2)