Need help with question 1 to 4

1. Find the area of the triangle formed when the following points are connected: A = (1, 0, 0), B = (0, 2, 0), and C = (0, 0, 3). 2. Give a vector equation for the line that passes through the point P = (2, -3, -1) and is normal to the plane 4x - y + 3z = 12. 3. Find the normal equation for the plane that contains lines La and Cb if both are defined for t E R by: La : ra(t) = ( 1 - 2t, -t, 2 + t) and Lb : rb(t) = (1 - t, t, 2 + 2t) 4. Roughly sketch the following functions and classify the surface (i.e. as a plane, sphere, ellipsoid, hyperboloid of 1 or 2 sheets, paraboloid, cone, cylinder, etc - refer to the lecture notes for more details) (a) z =12 + y2 - 2 in R 3 (b) (2 + 1)2 = 12 + 2 in IR3