- #1

Kernul

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- 7

## Homework Statement

Given the points ##A (1, -1, 0)## and ##B (4, 0, 6)##, find the point ##P## of the line ##s## so that the triangle ##ABP## is a right triangle in ##B##. Calculate the area of the triangle.

##s : \begin{cases}

x = 1 + 4t \\

y = 2 - 3t \\

z = 3

\end{cases}##

##\vec v_s = (4, -3, 0)##

## Homework Equations

## The Attempt at a Solution

I already know how to calculate the area of a triangle. The problem is actually finding the point that makes the triangle. I really have no idea on how to proceed in this case. I was thinking about finding the distances of the two points from the line but I don't think that would bring me anywhere. I tried finding the directional vector of the line that passes through the two points, which is ##\vec v_{AB} = (3, 1, 6)##, and find the relation between the two lines, maybe finding the intersection point too but it's useless. I really don't know where I should start. Any hint on how I should proceed?