Question

The displacement vectors A and B shown in the figure above both have magnitudes of 6.00 m. The direction of vector A is 0 = 25.09. a. Give the Cartesian coordinates of both vectors. Calculate the polar coordinates of: b. A - B c. A + B d.ShowĀ + BandĀ – 2B onadiagram. e. There are two vectors, Ū = -2î + 5 and V = -6i - kj where k is some number. The magnitude of is twice as big as the magnitude of Ū, i.e., V = 2 ŪL. Calculate the possible values for k.

Answer 1

magnitude of both Vector= om So, Š = 6 Å = 6 cos o î to sinofi a 6 cos 25 i tosin 25 i = 5.43 i + 2.54

- a Carte Cartesian Corordinates of rector à 21544-. ->(5.43, 2:54) 0,05 5.43 5:43 a (6) Å - = = 5:43 î + 2.549 - 61 = 5:43î - 3.46 |Ỷ - 3 = 3 = V[S + 3 + 3 4 5 = 6.438 and os tam" (= 3.468 = -32.50 So, plane polar co-ordinate of Å B is (6.44,-32.50 ) lg,o) 15:43

4) 4 +8 - 43 + 5q + 3 = 5:43 +8.54 | Athl=r= (5.482+ 8.54²)2 = 10.120 A Lama 8.54 O tomu leo ) 5.43 = 57.550 palar co-ordinate (5,0) = (10.120,57:55) d) À 4760,254 1 à (6.43,854). d) Å tě 16% . of 45:43,0) Ä - 2 (5.43,2.54) (0,4 (0-61 6:43, o) - -2B