Solve Vector Question: Find Shortest Distance from Point C to Line 1

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To find the shortest distance from point C to line 1, the line segment connecting C to point P on line 1 must be perpendicular to line 1. The problem can be solved using established formulas found in most calculus textbooks. It's important to note that the position of point C is given as (2i - k), and it does not lie on line 2, which is a common misconception. The relevance of line 2 in this context is minimal for calculating the distance. The solution is straightforward once the correct approach is applied.
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Hi, I haven't done vectors in a while and just wondering if someone could refresh my memory in solving this question for me:

line 1: r = (i + 2j - 3k) + m(4i - 5j -3k)

line 2: r = (4i - 4j + 3k) + n(i - 2j + 2k)

Point C with pos. vector (2i - k) lies on line 2. Find the shortest distance from C to line 1

Cheers, ul probs find this no probs!

Pat
 
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the line segment joining C with a point P on line 1 must be normal on line 1 in order to yield the shortest distance
 
Check the wording of the problem again. It is fairly straight forward to find the distance from point C to line 1 (most calculus books have a formula) and line 2 is completely irrelevant- but C is NOT on line 2!
 

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