A line passes through the point (2,1,-3) and is parallel to the vector `(hat(i) -2hat(j) +2hat(k))` . Find the equations of the line in vector and Cartesian forms .

A line passes through the point (3,4,5) and is parallel to the vector (2hat(i) +2hat(j) -3hat(k)) . Find the equations of the line in the vector as well as Cartesian forms.

A line passes through the point A(5,-2.4) and it is parallel to the vector (2hat(i) -hat(j) +3hat(k)) .The vector equations of the line is

Find the equation of the line through the point (1,2,0) and is parallel to the vector 2hat(i)+3hat(j)-5hat(k) .

Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3hat(i)+2hat(j)-2hat(k) .

A line passes through the point with position vector 2hat i-3hat j+4k is in the direction of 3hat i+4hat j-5hat k. Find the equations of the line in vector and Cartesian forms.

A line is drawn in the direction of (hat(i) +hat(j) -2hat(k)) and it passes through a point with position vector (2hat(i) -hat(j) - 4hat(k)) .Find the equations of the line in the vector as well as Cartesian forms.

(A ) Find the vector and cartesian equations of the line through the point (5,2,-4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8 hat(k) . (b) Find the equation of a line passing through the point P(2, -1, 3) and perpendicular to the lines : vec(r) = (hat(i) + hat(j) - hat(k) ) + lambda (2 hat(i) - 2 hat(j) + hat(k)) and vec(r) = (2 hat(i) - hat(j) - 3 hat(k) ) + mu (hat(i) + 2 hat(j) + 2 hat(k)) .

Find the vector equation for the line which passes through the point (1, ,2 3) and parallel to the vector hat i-2 hat j+3 hat kdot reduce the corresponding equation in the Cartesian from.

Find the vector equation for the line which passes through the point (1, ,2 3) and parallel to the vector hat i-2 hat j+3 hat kdot reduce the corresponding equation in the Cartesian from.