Embibe Experts Solutions for Exercise 8: Assignment

A line $L_1$ with direction ratios passes through the point $A\left(7,6,2\right)$ and a line $L_2$ with direction ratios passes through the point $B\left(5,3,4\right)$. A line $L_3$ with direction ratios $\left(2,-2,-1\right)$ intersects $L_1$ and $L_2$ at $C$ and $D$

A line parallel to $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and intersects the lines $9x+y+z+4=0=5x+y+3z ; x+2y-3z-3=0=2x-5y+3z+3$, then which of the following is/are correct?

The line $L$, passing through $M\left(1,1,1\right)$, and intersects at right angle to the line of intersection of the planes $x+2y-4z=0$, and $2x-y+2z=0$, then which of the following is/are correct?

Given plane $P_1=x+2y+2z=9$ and $P_2 \equiv 4x-3y+12z=-13$, then

The plane containing two lines $\frac{x-3}{1}=\frac{y-2}{4}=\frac{z-1}{5}$, and $\frac{x-3}{1}=\frac{y+3}{-4}=\frac{z-1}{5}$, is $10x+qy+rz=28$, where $\left(p=10\right)$, then

The line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects $xy=c^2, z=0$. Then possible value(s) of $c$ is/are

The intercepts made on the axes by the plane which bisects the line joining the points $\left(1,2,3\right)$ and $\left(-3,4,5\right)$ at right angles are $\alpha ,\beta ,\gamma$, then which of the following is correct?

The line $x=y=z$ meets the plane $x+y+z=1$ at the point $A$ and the sphere $x^2+y^2+z^2=1$ at points $B$ and $C$ then