If the angle between the planes $a x-y+3 z=2 a$ and $3 x+a y+z=3 a$ is $\frac{\pi}{3}$, then the direction ratio of the line perpendicular to the plane $(a+2) x+(a-4) y+2 a z=a$ are

The number of values of ' $k$ ' for which the points $(-4,9, k),(-1,6, k),(0,7,10)$ from right-angled isosceles triangle is

A line makes angles $60^{\circ}, 45^{\circ}, \theta$ with positive $X, Y, Z$ axes respectively. If $\theta$ is an acute angle, then $\tan \theta=$

If the foot of the perpendicular drawn from the point $(2,0,-3)$ to the plane $\pi$ is $(1,-2,0)$ and the equation of the plane $\pi$ is $a x+b y-3 z+d=0$, then $a+b+d=$