Find the equation of the plane which is parallel to the lines ` vec r= hat i+ hat j+lambda(2 hat i+ hat j+4 hat k)a n d(x+1)/(-3)=(y-3)/2=(z+2)/1""` and is passing through the point `(0,1,-1` ).

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 equation of a line passing through a point (2, -1, 3) and parallel to the line -> r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the equation of the plane parallel to hat i+hat j+hat k and hat i-hat j and passing through (1,1,2).

The image of the point (1,2,3) about the line vec r=(2hat i+3hat j-hat k)+lambda(hat i2hat j+2hat k) is

Find the vector equation of the line passing through (2,1,-1) and parallel to the line vec r=(hat i+hat j)+lambda(2hat i-hat j+hat k)* Also,find the distance between these two lines.

Find the equation of the line passing through the point hat i+ hat j- hat k and perpendicular to the lines vec r= hat i+lambda(2 hat i+ hat j-3 hat k)a n d vec r=(2 hat i+ hat j- hat k)dot

Find the vector equation of the line passing through (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 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.

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