Find the vector equation of the plane passing through the points having position vectors ` hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot`

Find the vector equation of the plane passing through three points with position vectors hat i+ hat j-2hatk, 2hat i-\ hat j+ hat k and hat i+2 hat j+ hat kdot Also find the coordinates of the point of intersection of this plane and the line vec r=3 hat i-\ hat j- hat k+lambda(2 hat i-\ 2 hat j+ hat k)dot

Find the vector equation of the plane passing through three points with position vectors hat i+ hat j-2hatk, 2hat i-\ hat j+ hat k and hat i+2 hat j+ hat kdot Also find the coordinates of the point of intersection of this plane and the line vec r=3 hat i-\ hat j- hat k+lambda(2 hat i-\ 2 hat j+ hat k)dot

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

Find the vector equation of the plane passing through the points 3 hat i+4 hat j+2 hat k ,2 hat i-2 hat j- hat ka n d7 hat i+6 hat kdot

Find the vector equation of a line which passes through the point with position vector 2 hat i= hat j+4 hat k and is in the direction of hat i+ hat j-2 hat kdot Also, reduce it to Cartesian form.

Find the vector equation of a line passing through a point with position vector 2 hat i- hat j+ hat k , and parallel to the line joining the points - hat i+4 hat j+ hat ka n d hat i+2 hat j+2 hat kdot Also, find the Cartesian equivalent of this equation.

Show that the points having position vectors 6 hat i-7 hat j ,\ 16 hat i-19 hat j-4 hat k ,\ 3 hat j-6 hat k ,\ 2 hat i+5 hat j+10 hat k are not coplanar.

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Find the vector equation of the plane passing through the intersection of the planes -> rdot(2 hat i+2 hat j-3 hat k)=7, -> rdot(2 hat i+5 hat j+3 hat k)=9 and through the point (2, 1, 3).

Find the vector equation of a line passing through the point with position vector hat i-2 hat j-3 hat k and parallel to the line joining the points with position vectors hat i- hat j+4 hat ka n d2 hat i+ hat j+2 hat kdot Also, find the Cartesian equivalent of this equation.