Math 215: Calculus 3, HW1 Due date: 9/19 or 9/21 1. Describe in words the region of R3 represented by x2 + z 2 = 25. 2. Write inequalities to describe the solid left (x < 0 is left) hemisphere of a sphere of radius 4 centered at the origin. a b copy the vectors and then 3. Given vectors a and b as in draw a + b,a b, a/2, 4b, and 2b a. 4. If a and b are as in the previous problem, sketch vectors c and d such that the sum of c and d is equal to a and their di\u001berence equal to b. 5. Find the coordinate representation of the vector joining A : (0, 4) and ~ and the same vector with starting point at the B : (3, 2). Sketch AB origin. 6. Suppose wind is blowing from N 45o W at a speed of 50 km/h. A pilot is steering the plane due North at an airspeed (speed relative to air) of 250 km/h. The true course is the direction of the sum of the two vectors and the ground speed is the magnitude of the resultant vector. Find the true course and the ground speed. 7. Find the value of x so that the angle between < 2, 1, 1 > and < 1, x, 0 > is 45o . 8. A tow truck drags a stalled car. The chain makes an angle of 30o with the road and the tension in the chain is 1500 Newtons. Find the work done by the tow truck in dragging the car for 1 km. 1 9. Find the angle between a diagonal of a cube and a diagonal of one of its faces. 2