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 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 plane,passing through the point (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 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 (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 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 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+2hat j-5hat k)+9=0

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

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.