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I have a vector $v_1$ (suppose $v_1= \langle a_1, b_1,c_1\rangle$) and this $v_1$ passes through the point $(x_1,y_1,z_1)$. Now I need a second vector, $v_2$ which is perpendicular to $v_1$. Suppose that $v_2$ is passing through the second point $(x_2,y_2,z_2)$. However, my final goal is to find the intersection point of above two lines. So, could you help me to find the vector which is perpendicular to another given vector? Please anyone help me.

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    ok, if i explain my question in another way;I have a point (x1,y1,z1) and a vector (a,b,c). This vector goes through that point. So, I am able to get the parametric equation of respective line. Now I have another point (x2,y2,z2) which locates closer to that line. If I draw another line, passing through (x2,y2,z2) and perpendicular to the above line, then what would be the coordinates of intersection point. That is what I am expecting at the end.2011-04-08

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Ok, so your line $\ell$ has parametric equations $ x=x_1+at,\qquad y=y_1+bt,\qquad z=z_1+ct. $ If $Q=(x_2,y_2,z_2)$ is a point, the equation of the plane $\pi$ perpendicular to $\ell$ and passing through $Q$ has equation $ a(x-x_2)+b(y-y_2)+c(z-z_2)=0. $ Now just plug the former equations into the latter and solve for $t$.

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    ok, thank you soo much. its clear now.2011-04-09
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Make a plane which is perpendicular to a given vector, then all vectors which lies on that plane will be perpendicular to that vector.