Show that the line of intersection of the planes ` vec rdot( hat i+2 hat j+3 hat k)=0a n d vec r=(3 hat i+2 hat j+ hat k)=0` is equally inclined to `ia n dkdot` Also find the angle it makes with `jdot`

Angle between hat i+hat j and the line of intersection of the planes vec r*(hat i+2hat j+3hat k)=0 and vec r*(3hat i+3hat j+hat k)=0 is equal to

Show that the following planes are at right angle: vec rdot((2 hat i- hat j+ hat k)=5\ a n d\ vec rdot((- hat i- hat j+ hat k)=3.

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i+3 hat j-6 hat k)=5\ a n d\ vec rdot(( hat i-2 hat j+2 hat k)=9.

Find the angle between the plane: vec rdot((2 hat i-3 hat j+4 hat k)=1\ a n d\ vec rdot((- hat i+ hat j)=4 .

Find the angle between the planes vec r*(2hat i-hat j+hat k)=6 and vec r*(hat i+hat j+2hat k)=5

The lines vec r=(hat i+hat j+hat k)alpha+3hat k and vec r=(hat i-2hat j+hat k)beta+3hat k

Find the equation of the plane passing through the intersection of the planes vec rdot( (hat i+ hat j+ hat k)=1\ a n d\ vec rdot((2 hat i+3 hat j- hat k)+4=0 and parallel to x-axis.

A vector parallel to the line of intersection of the planes vec r=dot(3 hat i- hat j+ hat k)=1\ a n d\ vec rdot(( hat i+4 hat j-2 hat k)=2 is a. -2 hat i+7 hat j+13 hat k b. 2 hat i+7 hat j-13 hat k c. -2i-7j+13 k d. 2i+7j+13 k

Find the equation of the plane through the line of intersection of the planes vec rdot(( hat i+3 hat j)+6=0\ a n d\ vec rdot((3 hat i- hat j-4 hat k)=0, which is at a unit distance from the origin.