Findthe equation of the line passing through points `hati-2hatj+hatk and -2hatj+3hatk` in vector form and Cartesian form.

Find the equation of the line passing through point 2hati-hatj+3hatk and parallel to vector hati+hatj-2hatk in vector form as well as Cartesian form.

Find the vector equation of the plane passing through the point hati + hatj -2hatk and hati + 2hatj + hatk, 2hati - hatj + hatk.

Find the vector equation of the plane passing through the point (3hati+4hatj+2hatk) and parallel to the vectors (hati+2hatj+3hatk) and (hati-hatj+hatk) .

The vector equation of the plane passing through the points hati+hatj-2hatk,2hati-hatj+hatk and hati+hatj+hatk , is

Find the vector equation of the line passing through the point 2 hati + hatj - 3 hatk and perpendicular to the vectors hati + hatj + hatk and hati + 2 hatj - hatk .

Find the vector equation of a line passes through the point hati+3hatj+hatk and parallel to vector 3hati-2hatj+k .

Find the vector equation of the line passing through the point with position vector 2 hati - hatj + hatk and parallel to the line joining the points with position vectors - hati + 4hatj + hatk and hati + 2 hatj + 2 hatk . Also, find the cartesian equation of the line.

Find the vector equations of the line passing through the point having positions vector -hati -hatj +2hatk and parallel to the line overset(-) r = ( hati+ 2hatj + 3hatk ) +mu (3hati + 2hatj +hatk) , mu is a parameter .

Find the vector equation of the plane passing through a point having position vector 3hati - 2hatj + 3hatk and perpendicular to the vector 4hati + 3hatj + 2hatk .