Find the vector and cartesian equation of a line passes through the points `(1,3,2)` and origin.

Find the vector and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

Find the vector and cartesian equation of plane which passes through the point (1,3,-2) and normal to the vector (2hati+hatj-2hatk) .

Find the vector and cartesian equations of the line that passes through : the points (1,2,3) and (2,-1,4).

Find the vector and cartesian equation of the line passing through the point (2,1,3) and perpendicular to the lines. (x-1)/(1)=(y-2)/(2)=(z-3)/(3) and (x)/(-2)=(y)/(2)=(z)/(5)

(i) Find the vector and cartesian equation of the line passing through the point (1,2,-4) and perpendicular to the two lines : (x - 8)/(3) = (y + 19)/(-16) = (z - 10)/(7) and (x - 15)/(3) = (y - 19)/(8) = (z - 5)/(-5) . (ii) Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicular to the lines : (x -1)/(1) = (y -2)/(2) = (z - 3)/(3) and (x)/(-3) = (y)/(2) = (z)/(5) .

Find the vector and cartesian equations of the line passing through the point (2,1,3) and perpendicualr to thelines : (x-1)/1=(y-2)/2=(z-3)/3 and x/-3=y/2=z/5

Find the vector and cartesian equations of the plane that passes through the point (1,0,-2) and normal to hati+hatj-hatk .

Consider the points A(3,-4,-5) and B(2,-3,1) Find the vector and Cartesian equation of the line passing through the points A and B.

Find the vector and cartesian equation of the plane passing through the point (1,2,3) and perpendicular to the line with direction ratio lt2,3,-4gt .