Foot of Perpendicular of a Point on a Line

Q.

Find the co-ordinates 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)___

1. $(\frac{-5}{3},\frac{2}{3},\frac{19}{3})$
   

2. $(2,-3,-1)$
3. $(1,-2,1)$
4. $(\frac{1}{2},-\frac{3}{2},2)$

Q.

Find the co-ordinates 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)___

1. $(\frac{-5}{3},\frac{2}{3},\frac{19}{3})$
   

2. $(2,-3,-1)$
3. $(1,-2,1)$
4. $(\frac{1}{2},-\frac{3}{2},2)$

Q. The distance of the point $P(-2,3,-4)$ from the line $\frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}$ measured parallel to the plane $4x+12y-3z+1=0$ is $d$, then the value of $(2d-8)$ is

Q.

Let the foot of the perpendicular of $P(2,-3,1)$ on the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-2}{-1}$ be $Q.$
If direction ratios of the line segment joining P and Q be $l,m,n$, then which of the following relations are correct ?

1. $2l+3m+n=1$

2. $2l+3m-n=0$

3. $\frac{l}{2}=\frac{m}{3}=\frac{n}{-1}$

4. $\frac{l}{2}=\frac{m}{3}=\frac{n}{1}$

Q. The co-ordinates of the foot of perpendicular drawn from point P(1, 0, 3) to the line joining the points A(4, 7, 1) and B(3, 5, 3) is

1. $(5,7,1)$
2. $(\frac{5}{3},\frac{7}{3},\frac{17}{3})$
3. $(\frac{2}{3},\frac{5}{3},\frac{7}{3})$
4. $(\frac{5}{3},\frac{2}{3},\frac{7}{3})$

Q.

The point P is the intersection of the straight line joining the points Q (2, 3, 5) and R (1, -1, 4) with the plane 5x-4y -z = 1. If S is the foot of the perpendicular drawn from the point T (2, 1 , 4) to QR, then the length of the line segment PS is

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

2. $\sqrt{2}$
   

3. 2

4. $2\sqrt{2}$

Q.

Let the foot of the perpendicular of $P(2,-3,1)$ on the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-2}{-1}$ be $Q.$
If direction ratios of the line segment joining P and Q be $l,m,n$, then which of the following relations are correct ?

1. $2l+3m+n=1$

2. $2l+3m-n=0$

3. $\frac{l}{2}=\frac{m}{3}=\frac{n}{-1}$

4. $\frac{l}{2}=\frac{m}{3}=\frac{n}{1}$

Q. The foot of the perpendicular from P(1, 0, 2) to the line $\frac{x+1}{3}=\frac{y-2}{-2}=\frac{z+1}{-1}$ is

1. $(1,2,-3)$
2. $(\frac{1}{2},1,-\frac{3}{2})$
3. $(2,4,-6)$
4. $(2,3,6)$

Q. The foot of the perpendicular from (0, 2, 3) to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is :

1. (3, 2, –1)
2. (–2, 3, 4)
3. (2, –1, 3)
4. (2, 3, –1)

Q. The foot of the perpendicular from (0, 2, 3) to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is:

1. (–2, 3, 4)
2. (2, –1, 3)
3. (2, 3, –1)
4. (3, 2, –1)