If the image of the point $(4,4,3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha, \beta, \gamma)$,then $\alpha+\beta+\gamma$ is equal to

If $L_1$ is a line through the point $5 \hat{i}+8 \hat{j}+11 \hat{k}$ and parallel to the vector $2 \hat{i}+3 \hat{j}+4 \hat{k}$ and $L_2$ is a line through the point $4 \hat{i}+6 \hat{j}+8 \hat{k}$ and parallel to the vector $3 \hat{i}+4 \hat{j}+5 \hat{k}$, then the point of intersection of $L_1$ and $L_2$ is

The line joining points $(3, 5, -7)$ and $(-2, 1, 8)$ meets the $yz$-plane at which point?

The Cartesian equation of the line which is parallel to the line $\frac{x+3}{3}=\frac{y-4}{5}=\frac{z+8}{6}$ and passing through the point $(1, -3, 5)$ is:

If the direction cosines of two lines are given by $l+m+n=0$ and $mn-2lm-2nl=0$,then the acute angle between those lines is

The equation of the line passing through the point $(3,1,2)$ and perpendicular to the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$ is