Find the equation of plane passing through the point ` hat i+ hat j+ hat k` and parallel to the plane ` vecr.(2 hat i- hat j+2 hat k)=5.`

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the vector and cartesian equations of the line passing through the point P\ (1,\ 2,\ 3)\ and parallel to the planes vec rdot( hat i-\ hat j+2 hat k)=5\ and vec rdot(3 hat i+ hat j+ hat k)=6.

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)=5 and vec rdot(3 hat i+ hat j+ hat k)=6.

Find the vector and Cartesian forms of the equation of the plane passing through the point (1,\ 2,\ -4) and parallel to the lines vec r=( hat i+2 hat j-4 hat k)+lambda(2 hat i+3 hat j+6 hat k)a n d\ vec r=( hat i-3 hat j+5 hat k)+mu( hat i+ hat j- hat k)dot Also find the distance of the point (9, -8, -10) from the plane thus obtained.

Find the equation of the plane passing through (a ,b ,c) and parallel to the plane vec r is dot( hat i+ hat j+ hat k)=2.

Find the equation of a line passing through a point (2, -1, 3) and parallel to the line vec r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the vector equation of the line passing through (1, 2, 3 ) and parallel to the planes vec rdot( (hat i- hat j+2 hat k)=5\ a n d\ vec rdot((3 hat i+ hat j+ hat k)=6.

Find the distance of the point 2 hat i+ hat j- hat k from the plane vec r( hat i-2 hat j+4 hat k)=9 .

Find the distance of the point 2 hat i- hat j-4 hat k from the plane vec rdot((3 hat i-4 hat j+12 hat k)-9=0.

Find the equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.