Equation of a Plane : Normal Form

Q.

The equation of the plane containing the two lines $\frac{(x-1)}{2}=\frac{(y+1)}{-1}=\frac{z}{3}$and$\frac{x}{-1}=\frac{(y-2)}{3}=\frac{(z+1)}{-1}$ is

1. $8x+y–5z–7=0$

2. $8x+y+5z–7=0$

3. $8x–y–5z–7=0$

4. None of these

Q.

If $p=i+j,q=4k-j,\text{and}r=i+k$ then the unit vector in the direction of $3p+q-2r$ is?

1. $\frac{1}{3}\left(i+2j+2k\right)$

2. $\frac{1}{3}\left(i-2j-2k\right)$

3. $\frac{1}{3}\left(i-2j+2k\right)$

4. $\left(i+2j+2k\right)$

Q.

Equation of the plane which passes through the point of intersection of lines $\frac{x-1}{3}=\frac{y-2}{1}=\frac{z-3}{2}$ and $\frac{x-3}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ and at the greatest distance from the point (0, 0, 0) is

1. $4x+3y+5z=25$

2. $4x+3y+5z=50$

3. $3x+4y+5z=59$

4. $x+7y-5z=2$

Q.

Find the equation of plane which is at a distance of 8 units from the origin and which is normal to the line having direction ratios 2, 1, 2 ?

1. x + 2y + z = 24

2. 2x + y + 2z = 24

3. 2x + 2y + z = 72

4. x + 2y + 2z = 72