- #1

Krushnaraj Pandya

Gold Member

- 697

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## Homework Statement

Suppose a line is given, say (x-3)=(y-2)=z in Cartesian form and we are supposed to find a point on it which is at a distance say, 6 units from a given arbitrary point (1,2,3).

**2. Relevant tedious methods**

1) write line in vector form then equate modulus of vector between point on line and given point to 6

2)use given equation and distance formula to get the point.

## The Attempt at a Solution

Using vector form of line as well using distance formula is very tedious and has high chances of calculation mistakes and its a really off-putting thing especially in exam pressure when you put a lot of time into it and still get a wrong answer, I would be glad if the people on PF could brainstorm a shorter, faster way to arrive at this-perhaps calculus could help in some way. Thank you for your help.