Question

[3] Given: u = -81 + 6j v = 1-3 w = 41 - 8j T= -101 Point Pat (-7, -2), point at (-9, 11), and point Rat (8.-15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in x + yj form, for the vector whose initial point is R and whose terminal point is g. b) Sketch the position vector determined by point P, and then find its magnitude and direction. Sketch (1 pt): Magnitude (2 pts): Direction (2 pts): c) Find t in (x, y) form if t = 6u - 3v + - T. d) Find t in x + yj form such that the magnitude oft is 10 and the direction oft is 200 degrees. Round the horizontal (x) and vertical component (y) to the nearest tenth. e) Find the angle between vectors u and w. f) Find the dot product of the following two vectors: 2u - 4v and -w

Answer 1

san Given W = 44-81 U= -8u+6j V=j-j T: -100 foient P (-57,-2) 6. (-9,11) R: (8,-15) ay Initial Point (R)= 18, -15) Toreimal Point (6)= (-9.11) Position vector (&q-X,) u + (92), ) j (-9-8)j + (11-(-15)) ; = -171 +263 b) Point (P) = (-81-82) Puri-Vaj 1 Pl: vivi)'(-vă)? V7+2 - 13 Direetim tamil -12 f 28-13° but Point lies in god Quadrant So, O= 180° +28.13° 5208:13 28 13 (-17,-12)

et = 60-3V+W-8 = 6(-86 +61) -3 (1-j) + (40-8i)-(-105) = -484 +36 j - 3j+31 +46-8j+100 -374 +319 so t= -374 +3 11 dy Given let1 = 10 and 0- 200° SO 10 COS 20° 200 20° K10 10 y losim 20° X-component = 10 cos 209 9.396 9.4 Yo component 10 sim 20° 3.4 Here o dies im god Quadrant 30. X.and y valuus is megalive. so, x = -9.4 y=-3-4 et = -9.40 -3.4j el Angle between two vetor u and w Cos 0 = U.W Jul Jul = V1-899 +(6) lwl - V143*+(-3)? V (43²+ (-8)² = 455 = 10

U.W= (-81 +63) (44-83) - 8x4 +68-8 -32 - 48 - 80 -80 Coso = 10 X 415 .: 0= cos" (7006) 153.4° f} dot Product of 20 - 4V and - Wto X = 20 - 4V = 2(-8j+6j)- 4 (0-3) 5.-160412 3 - 41+41 - 204 + 16) Y: -W+ = - (4 ;-81) + (-10 i ) - 44+8j-lou = -14° +8] x.y = (-200 + 163) (-14 i +80) -20%-14 +16x8 280 + 128 408