[" 1.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.

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 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 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 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 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 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 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.