A line passes through the point with position vector `2hati-hatj+3hatk` and is in the direction of `hati+hatj-2hatk`. Find the equation of the line in vector and Cartesian forms.

The vector equation of a line passing through the point with position vector 2hati - hatj - 4hatk and is in the direction of hati - 2hatj + hatk is

The cartesian form of equation of a line passing through the point with position vector 4hati -hatj +2hatk and is in the direction of -2hati +hatj +hatk ,is

Find the vector equation of a line which passes through the point with position vector 4hati - hatj + 2 hatk and is in the direction of - 2 hati + hatj + hatk .

Find the vector equation of a plane passing through a point having position vector (2hati-hatj+hatk) and perpendicular to the vector (4hati+2hatj-3hatk) . Also, reduce it to Cartesian form.

The points with position vectors 5hati + 5hatk, -4hati + 3hatj - hatk and 2hati +hatj + 3hatk

Find the equation of the line in Cartesiasn form that passes through the point with positoin vector 2hati-hatj+4hatk and is in the direction hati+2hatj-hatk.

Find the equation of a line passes through the points whose position vectors are (hati+4hatj+hatk) and (2hati-hatj+5hatk) .

Find the vector equation of the plane passing through three points with position vectors hati + hatj - 2 hatk, 2 hati - hatj + hatk and hati + 2 hatj + hatk . Also find the co-ordinates of the point of intersection of this plane and the line vec(r) = 3 hati - hatj - hatk + lambda (2 hati - 2 hatj + hatk) .

Find the vector equation of a line passing thorugh a point with position vector 2hati-2hatj+hatk and parallel to the line joining the point with the position vectors -hati+3hatj+hatk . Also find the Cartesian equation of this line.