Write the vector equation of the plane, passing through the point (a,b,c) and parallel to the plane ` vec rdot( hat i+ hat j+ hat k)=2.`

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

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane vec rdot((2 hat i+ hat j+2 hat k)=5.

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

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

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

Find the vector and Cartesian equations 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 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 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 plane passing through the point (3,0,-2) and parallel to the planes 3hat i-4hat j and 2hat j+5hat k

Find the equation of lane passing through the point hat i+ hat j+ hat k and parallel to the point -> rdot(2 hat i- hat j+2 hat k)=5.