Question

Please help me to solve question #47 and #53.

v with the given magnitude In Exercises 47-50, find the vector v with the . and the same direction as u. Magnitude (47) || v || = 4 48. || v || = 4 49. || v || = 2 50. || v || = 3 Direction u = (1,1) u = (-1,1) u = (V3, 3) u = (0,3) In Exercises 51-54, find the component form of v given is magnitude and the angle it makes with the positive x-axis. 51. || \ || = 3, 0 = 0° 52. || v || = 5, 6 = 120° ( 53. || v || = 2, 0 = 150° 54. || v || = 1, 0 = 3.5°

Answer 1

Solue + We know that a given magnitude Ivi and of u, is given by the in vector v with the direction ll U11 Here U= <1,1> 101 = V(u2+(012 - Võ and Vll= 4 Therefore V = < I > Ilull VET = < 202, 2v7) V 2

Solve - The component form of v, having magnitude 101 and angle with positive x-anis is - < 11V11 losio), ll V11 sinlol > Here 11111 = 2: and 0 = 150° IIVIT sin(o) III LO O) : Juil Loslo= 2 los (150) = 2 los (90'+60') :: Los ( 90+0) = - 2 sin (60) = sino) = -21%) = -V3

And Ilul sinlos = 2 sin (150') = 2 sin (90+60) = 2 101160') = 2() Thus component form of v is <-3,1)
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