There is given a vector 2i+j-3k and now I want to find the equation of a line that is perpendicular to the given vector and passing through a known point (1,1,1) .How can I solve this ?.
So, you are given the vector (2,1,-3). Let (2k,k,-3k) be the orthogonal projection of (1,1,1) on (2,1,-3). Then, (2k-1,k-1,-3k-1) and (2,1,-3) are orthogonal, giving: 4k-2+k-1+9k+3=0 i.e. k=0. So, (0,0,0),the origin is the projection. Hence, the line contains the points (0,0,0) and (1,1,1), so its equation is x=y=z, if my calculations are correct!