Find the Cartesian equation of a line which passes through the point having position vector `(2hat(i) -hat(j) + 4hat(k)) ` and is in the direction of the vector ,`(hat(i) +2hat(j) -hat(k))`

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

Find the vector equation of a line which passes through the point with position vector hat(i)-2hat(j)+4hat(k) and is in the direction of hat(i)+2hat(j)-hat(k) . Also, reduce it to cartesian from.

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

Find the vector equation of a line passing through the point having the position vector (hat(i)+2hat(j) -3hat(k)) and parallel to the line joining the points with position vectors (hat(i) -hat(j) +5hat(k)) and (2hat(i) +3hat(j) -4hat(k)) .Also find the Cartesian equivalents of this equations.