Straight Lines ...

The coordinates of the foot of perpendicular drawn from the point $$A(1,\ 8,\ 4)$$ to the line joining the points $$B(0,\ -1,\ 3)$$ and $$C(2,\ -3,\ -1)$$. 

Two points A$$\left ( x_{1},y_{1} \right )andB\left ( x_{2},y_{2} \right )$$ are chosen on the graph of $$f(x)=inx with 0<x_{1}<x_{2}.$$ the point C and D trisect line segment AB with AC<CB. through Ca horizontal line is drawn to cut the curve at$$E\left ( x_{3},y_{3} \right ).if x_{1}=1000$$then the value of$$x_{3}$$ equals

Find the relation between $$x$$ and $$y$$ such that the point $$P(x, y)$$ is equidistant from the points $$A(1, 4)$$ and $$B(-1, 2)$$.

If the line $$\left( \cfrac { x }{ 2 } +\cfrac { y }{ 3 } -1 \right) +\lambda(2x+y-1)=0$$ is parallel to x-axis then $$\lambda=$$

The length of the median from the vertex $$A$$ of a triangle whose vertices are $$A ( - 1,3 ) , B ( 1 , - 1 )$$ and $$C ( 5,1 )$$ is

The midpoints of the sides of a triangle are $$\left(1,1\right),\left(4,3\right)$$ and $$\left(3,5\right)$$. The area of the triangle is ___ square units.

The angle between the lines $$x\cos{30}^{o}+y\sin{30}^{o}=3$$
$$x\cos{60}^{o}+y\sin{60}^{o}=5$$ is

The points$$ (0,1), (-2,3), (6,7), (8,3)$$ form 

If $$ B (1, 3) $$ is equidistant from $$ A (6,  -1) $$ and $$ C (x, 8) $$, then  $$ x =$$

If $$x+4y=7$$, where $$y\ \in\ N$$, then the minimum positive value of $$x+y$$ equals