12. Vectors A, B, and & have a length of 6 cm, 4 cm, and 2 cm, respectively, and they are oriented as shown in the figure. Let R = A + B + C a) Calculate the x and y components of R. Hint: calculate the x and y components of all the vectors. b) Calculate the magnitude and direction of R. B Чем 50° 2cm y 6cm 30°

4. Right handed coordinate system: In a three dimensional coordinate system we can always choose +x and +y to be in any direction we want as long as they are perpendicular. For a right handed coordinate system we always choose the +2 direction so that i xj is in the +2 direction. Use the right-hand rule to determine the following vector products. ixi ixj îxk & jxi kxi jxj kxj 0 -1 jxk kxk +y +X 5. Assume we have two vectors Ā= A¸Î + A‚Ĵ + Ak and B = B¸î + B,Ĵ + B. We can use the rules for the cross products of the unit vector write the cross product AxB in terms of its' components as Ax B= (A,B₂ - A,B,) i — (A_B_ — A‚B‚)Ĵ + (A_B‚ — A,B.) k Example: A force = (20 - 2j+5k) N is drone at vector F = (21 +3)) m measured from the center of mass of the drone. In flight, the center of mass is the axis of rotation. Determine the torque exerted by this force. Express your answer using unit vectors Starting steps: 7=7 x = (2î +3ĵ) m× (20î − 2j+5k) N

For the vectors V1 = 10 units and V2 = 7,5 units shown in the figure, V1 45° - X 30° V2

Three vectors A, B and C add together to yield zero, i.e. A + B + C = 0. The vectors A and C point in opposite directions and their magnitudes are related by the expression: A = 2C. Which one of the following conclusions is correct? A. A and B have equal magnitudes and point in opposite directions. B. B and C have equal magnitudes and point in the same direction. C. A and B point in the same direction, but A has twice the magnitude of B. OD. B and C point in the same direction, but C has twice the magnitude of B. E. A and B