Two vectors are given by a = 8.07 + 5.9j and b = 1.97 + 8.7. Find (a)|a x b , (b) d . b, (c)( a + b ) . b, and (d) the component of a along the direction of b ? (a) Number i Units V (b) Number Units V (c) Number i Units V (d) Number Units VUse the definition of scalar product, a . b = ab cos 0, and the fact that a . b = axbx + ayby + azz to calculate the angle between the two vectors given by a = 7.0i + 7.0j + 7.0k and b = 5.07 + 7.0j + 6.0k. Number i UnitsRock faults are ruptures along which opposite faces of rock have slid past each other. In the gure, points A and B coincided before the _> _> rock in the foreground slid down to the right. The net displacement AB is along the plane of the fault. The horizontal component of AB > is the strikeslip AC. The component of AB that is directly down the plane ofthe fault is the clip-slip AD. (3) What is the magnitude of the > net displacement AB if the strike-slip is 22.0 m and the dip-slip is 16.6 m? (b) If the plane of the fault is inclined at angle 99 = 47 to the horizontal, what is the magnitude of the vertical component of E ? Silikc-slip Dip-slip Fault plant. (a) Number a Units V (b) Number n Units V What are (a) the x component, (b) the y component, and (c) the z component of 7 = a - b + c if a = 8.7i + 1.1] - 2.5k, b = - 6.27 + 4.2 j + 7.2k, and c = 8.37 + 6.9j + 3.7k. (d) Calculate the angle between 7 and the positive z axis. (e) What is the component of a along the direction of b ? (f) What is the magnitude of the component of a perpendicular to the direction of b but in the plane of a and b ? (a) Number Units (b) Number i Units (c) Number Units (d) Number Units (e) Number i Units (f) Number UnitsA bank in downtown Boston is robbed (see the map in the gure). To elude police, the robbers escape by helicopter, making three successive ights described by the following displacements: 32 km, 45 south of east; 53 km, 26 north of west; 26 km, 18 east of south. At the end of the third ight they are captured. In what town are they apprehended