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# Scalar product application? watch

1. Using the scalar product, calculate the shortest distance between the point (1, 2, 3) and the line that passes through the points (1, 1, 1) and (2, 3, 1).

How can this be done without the cross product?

Thanks
2. You should be able to find a parametric vector equation for the straight line that passes through those points.

Let (a,b,c) be the point on that line which is closest to (1,2,3). You should be able to write (a,b,c) in a particular parametric form. You should therefore be able to find the vector from (1,2,3) to (a,b,c), again in a form that includes a parameter. This vector must be perpendicular to the line (why?). Can you now use the cross product to finish off?
3. (Original post by runny4)
Using the scalar product, calculate the shortest distance between the point (1, 2, 3) and the line that passes through the points (1, 1, 1) and (2, 3, 1).

How can this be done without the cross product?

Thanks
4. Thank you
5. if you have a vector perpendicular to a line, then the dot product of that vector with the direction vector of the line must = 0

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Updated: January 8, 2017
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