1. Vector Operations. Let u = 2j+3k and = 2+ 3+k and w=i-j+ k. Find (a) . v, (b) u xv, || x ||- area of parallelogram with sides 7 & 7 (c) || xv|||||||||||sin (0)| (d) Proj (e) 3 v (2+ 3v) v (f) the angle between 7 and 7, cos(0) = (-v)/(|||||||| (g) - (u v) - tripe scaler product, volume of parallel piped with sides u, v & 2. Lines, Planes and Quadric Surfaces (a) Find the equation of the line going through the points (1,2,0) and (4,5,6). (b) Find the equation of the plane going through the points (2,0,1), (0, 4, 1) and (-1,-1,0). (c) Find the point of intersection of the line r(t) (2t + 1,3t2, t + 1) and the plane x-3y + 2z = 7. (d) Find the angle between the line r(t) = (2t+1,3t-2, t+1) and the plane r-3y+2z = 7. (e) Find the distance between the point P = (3,-2, 6) and the plane -2r+ y 32 = 4. (f) Use intercepts to sketch the plane 2r + 4y + 8z 16. (g) Sketch the surface z = 5- (r + y). What type of quadric surface is this? (h) Sketch the surface z = 3+ + y. What type of quadric surface is this? (i) Sketch the surface z + 4y +9z = 36. What type of quadric surface is this? (j) What is the difference between r + y + z = 1 and r + y + z 1? 3. Motion along a 1D curve in R. Let an object follow the path r(t) = (2 cos 4t, 6t - 2, 2 sin 4t). Find (a) the velocity, speed and acceleration (b) the unit tangent and normal vectors (c) the curvature (d) the tangential and normal components of acceleration