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 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.

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 (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 -> rdot( hat i- hat j+2 hat k)=5\ a n d\ -> 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)a n d vec rdot(3 hat i+ hat j+ hat k)=6.

Find the angle between the planes vec rdot(2 hat i- hat j+ hat k)=6a n d vec rdot( hat i+ hat j+2 hat k)=5.

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

Find the angle between the plane: vec rdot((2 hat i- hat j+2 hat k)=6\ a n d\ vec rdot((3 hat i+6 hat j-2 hat k)=9.

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.