Find the vector equation of a lin e passes through the point whose position vector is `(2hati-hatj-hatk)` and parallel to vector `hati+5hatk`.

Find the vector equations of the line passing through the point having positions vector 4 hati -hatj +2hatk and parallel to the vector -2hati -hatj +hatk

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

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

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 a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Find the vector and cartesian equation of the plane through the point whose position vector is 2hati-3hatj+hatk and normal to the vector 3hati-2hatj-hatk .

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

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.

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