Distance between point and line (vectors)

Find the distance from the point A(7,6,10) to the line passing through B(3,7,0) and C(4,9,-2).

I know that the vector is and that the equation of the line is thus but I dont understand how you can find the distance between A and this line?

What you can try is to find the vector direction of AB. Then, find the angle CBA by using the dot product of the vectors.

Have a sketch, BC is a line, AB is another line. Draw the angle CBA. Drop a perpendicular line from A to line CB.

Now, the perpendicular line, AB and BM, where M is the point where the perpendicular meets BC is a triangle.

Have now a right angled triangle, an angle and you can find the length AB. Use

Quote:

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Originally Posted by SyNtHeSiS

Find the distance from the point A(7,6,10) to the line passing through B(3,7,0) and C(4,9,-2).

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Given a line and that then the distance from to is .