Chapter 2, Problem 83P

D1.3. The three vertices of a triangle are located at A(6, −1, 2), B(–2, 3, −4), and C(-3, 1, 5). Find: (a) RAB; (b) RAC; (c) the angle BAC at vertex A; (d) the (vector) projection of RAB on RAC. Ans. -8ax +4ay − 6az; −9ax +2ay + 3az; 53.6°; -5.94ax + 1.319ay + 1.979az

Vectors u = −10i + 3j and v = −7i − 9j. What is u − v?  a −17i − 6j  b 17i + 6j  c 3i − 12j  d −3i + 12j

Problem 4: Two points in a plane have polar coordinates P1(2.4 m, Jt/6) and P2(3.8 m, 2jt/3). P1(, y) m 20% Part (a) Determine the x value of the Cartesian coordinates for Pj.

Vector has a magnitude of 3 units and it creates an angle of 160° with the positive x-axis. Find the magnitude and direction of 57. Give the direction as an angle measure between 0° and 360°. ||5v|| = units 57 creates an angle of x-axis. O with the positive

Vector v = <-4,4> and vector w = <-2,-1>. Draw the vector v+w and give its component form.

Vector Quantity 60 30 15 A. A, 100 100 100 Vector Quantity 30 A, A. 173.2 100 3. At what angle will the x component equal the y component of a vector quantity?

B = 5.00 A=6.00 30.00 30.0 Two vectors (A and B) are shown in figure . The vector A-B is? 0.87i+ 5.51 O 1.7 i +0.5j O 1.7 i+5.51 9.53i+0.5 j 0-9.531-0.5 j Next

Problem 1: Vectors A and B are shown in Figure 1. a. What is A in terms of x and y components? Answer: A = 2.74î +7.52ĵ b. What is B in terms of x and y components? Answer: B = -18.13î - 8.45) c. What is the resultant vector R = A + B? Answer: R= -15.39î - 0.93ĵ d. What is R, the magnitude of R? Answer: R = 15.42 e. What is, the angle R makes with respect to the +x-axis? 0 = 180° +3.46° = 183.46° B Figure 1: Vectors for Problem 1. 25° B = 20 Ā A = 8 /70°

A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to try leaping it with his car. The side the car is on is 20.3 mm above the river, whereas the opposite side is a mere 1.6 mm above the river. The river itself is a raging torrent 57.0 mm wide. For help with math skills, you may want to review: Vector Magnitudes For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Different initial and final heights. a.  How fast should the car be traveling just as it leaves the cliff in order to just clear the river and land safely on the opposite side? Express your answer in meters per second. b.  What is the speed of the car just before it lands safely on the other side? Express your answer in meters per second.