Point Slope Form of a Line

Q.

If the foot of the perpendicular from point $(4,3,8)$ on the line $L_1:\frac{[x–a]}{l}=\frac{[y–2]}{3}=\frac{[z–b]}{4}$, $l\ne 0$ is $(3,5,7)$, then the shortest distance between the line$L_1$ and line $L_2:\frac{[x–2]}{3}=\frac{[y–4]}{4}=\frac{[z–5]}{5}$ is equal to:

1. $\frac{\sqrt{2}}{3}$

2. $\frac{1}{\sqrt{3}}$

3. $\frac{1}{2}$

4. $\frac{1}{\sqrt{6}}$

Q.

If the foot of the perpendicular from the origin to a straight line is at the point $\left(3,-4\right)$. Then, the equation of the line is

1. $3x–4y=25$

2. $3x-4y+25=0$

3. $4x+3y-25=0$

4. $4x+3y+25=0$

Q.

How do you know If two lines are perpendicular $?$

Q. Area bounded by lines $x-y+1=0$; $3x+2y-12=0$ and x-axis is k.Find 2k

Q. Let PS be the median of the triangle with vertices $P(2,2)$, $Q(6,-1)$ and $R(7,3)$. The equation of line passing through $(1,-1)$ and parallel to PS is :

1. $2x-9y-7=0$
2. $2x-9y-11=0$
3. $2x+9y-11=0$
4. $2x+9y+7=0$

Q. Two vertices of a triangle are $(5,-1)$ and $(-2,3)$. If orthocenter of the triangle is origin, then the co-ordinates of third vertex is

1. $(4,7)$
2. $(3,7)$
3. None of these
4. $(-4,-7)$

Q. Find the equation of the straight line whose $x$ and $y$-intercepts on the axes are given by $2$ and $3$

1. $3x-2y+6=0$
2. $3x+2y-6=0$
3. $3x-2y-6=0$
4. None of these