Find the vector equation of the plane passing through the points (3, 4, 2) and (7, 0, 6) and perpendicular to the plane `2x-5y-15=0.` Also, show that the plane thus obtained contains the line ` vec r= hat i+3 hat j-2 hat k+lambda( hat i- hat j+ hat k)dot`

Find the vector equation of the plane passing through the points (2,\ 1,\ -1)\ a n d\ (-1,\ 3,\ 4) and perpendicular to the plane x\ -\ 2y+4z=10 . Also show that the plane thus obtained contains the line vec r=- hat i+3 hat j+4 hat k+lambda\ (3 hat i-2 hat j-\ 5 hat k)dot

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to the plane 3x-4y+5z=8.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0 .

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane -> r(dot( hat i+2 hat j-5 hat k))=9.

Write the vector equation of the line passing through (1,2,3) and perpendicular to the plane vec r.( hat i+2 hat j-5 hat k)+9=0.

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

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 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 vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

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.