For a positive real number $p$, if the perpendicular distance from a point $-\hat{\mathbf{i}}+p \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ to the plane $\mathbf{r} \cdot(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}})=7$ is 6 units, then $p=$

If $Q(\alpha, \beta, \gamma)$ is the harmonic conjugate of the point $P(0,-7,1)$ with respect to the line segment joining the points $(2,-5,3)$ and $(-1,-8,0)$, then $\alpha-\beta+\gamma=$

On a line with direction cosines $l, m, n, A\left(x_1, y_1, z_1\right)$ is a fixed point. If $B=\left(x_1+4 k l, y_1+4 k m, z_1+4 k n\right)$ and $C=\left(x_1+k l, y_1+k m, z_1+k n\right)(k>0)$, then the ratio in which the point $B$ divides the line segment joining $A$ and $C$ is

If the line of intersection of the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$ makes an angle $\alpha$ with the positive $X$-axis, then $\cos \alpha=$