If $Q(1,0,1)$ is the image of the point $P(a, b, c)$ in the line $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$ then $a+b+c$ is equal to :

Shortest distance between the lines $\vec{r}=(8+3 \lambda) \hat{\imath}-(9+16 \lambda) \hat{\jmath}+(10+7 \lambda) \hat{k}$ and $\vec{r}=15 \hat{\imath}+29 \hat{\jmath}+5 \hat{k}+\mu(3 \hat{\imath}+8 \hat{\jmath}-5 \hat{k})$ is

P is a point on the line joining the points $(3,5,-1)$ and $(6,3,-2)$. If $y$ coordinate of point P is 2 , then $x$ coordinate will be

The value of $\lambda$ for which the angle between lines $\vec{r}=\hat{\imath}+\hat{\jmath}+\hat{k}+p(2 \hat{\imath}+\hat{\jmath}+2 \hat{k})$ and $\vec{r}=(1+q) \hat{\imath}+(1+q \lambda) \hat{\jmath}+(1+q) \hat{k}$ is $\frac{\pi}{2}$