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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 ?.

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Instead of Cross product why can't we use the Dot product.Because the Dot product of any two perpendicular vectors are equal to 0. –  Thusitha May 13 '12 at 11:54
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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!

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Thanks...It helped me a lot. –  Thusitha May 13 '12 at 11:58
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