Question

[3] Given: u = -81 +6j vi- j = -101 Point Pat (-17, -v2), point 9 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): Marnitude (2 pts): Direction (2 pts): c) Find t in (x, y) form ift = 6u - 3v + w - r. 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. h) Find the dot product of the following two vectors: 2u - 4v and -w + T.

Answer 1

-10c gover, e=-sito vain; w=4i-8j, poent e at (-57,-2) Q at (-9, R at (8,-15) R 9) is i vector oz vector whose inefecel poent and terminal poent o RG position vector position of P R (-9,11) = (-17, 2) (8,-13) RO -rit doj b) 51 -52 P (-5, -52 dy

magnifeedle length of op ſero-og? Troue ✓ 7+2 9 3 Now tanco = pm OM -12 -17 tano 1.4.4 0.534 2.645 is o= 28.10° direction of vecfor is angle made the vecfor neith horizontal lene direction of op 180°40 180'+28.10° en lit quadsent 208.10° by e t = 6u- 3r twox --61-8ioj) -311-1) + yi-sj +10 -48 i +36 ĭ -3i+ 3itui-sit 10 -3717311

į. ta 10 d) geven magnitude of 1 ti <-37, 31 317 that direcfoon is 200° z z xityi oft: ſzty? a> x² + y² let noyt cei magnitude of i: 2 10 2 2 = ) x²+y 102 x²+y² = 100 tan ) t to es of soe! P (ivot 200° fan(200°) = sla у 21 y 0.363 x 0.363* >> 2 o cured 2 ya x+ 6-363x)=100 ?+ 0.1312 100 1.131*? 100 2 100 2 2 1:/3/

x2 + 100 1:13/ 5/3 88.417 2= £ 9.40 Ž + 9.4 0.36 3x ( 9.40) y= y + 3.412 y = I 3.4 i's the set 200 queeodent direction of vector vector lees in t = -9.4 i -3.4;