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- Consider vector A, with a magnitude of 3, and a vector B, with a magnitude of 2. Are the following relationships possible? If so, sketch a picture that shows an example of how they're possible, and identify all the angles between the vectors that make the relationship possible. (Exact angles, not decimal approximations. No calculators.) Relationship: Possible? Sketch: Angles: a. 1A+삐>5 b. A+ B| = 5 c. A+ B| = 1 d. A+미<1 - 1<|A+삐<5Vector A = 7.2 i + 2.6 j. Vector B = 7.5 i + 7.4 j. The magnitude of the cross product i.e. |AxB| is: :Component Method: With your calculator, determine the x and y components of F1 and F2. Remember that Fx = Fcos θ and Fy = F sin θ. Find the x and y components of the resultant from the sum of x and y components. Draw a right triangle with x and y components as sides, and the hypotenuse representing the resultant. Calculate the magnitude of the resultant from the square root of (Rx2 + Ry2). Calculate the direction of the resultant by using θ R = tan-1 (Ry/Rx).
- Vector C can be written (-3i+1j) cm O (-4i+2j) cm O (i-3j) cm (2i+-4j) cm 1 y (cm) 2 1 x (cm)Vector C has a magnitude of 24.6 m and points in the -y- direction. Vectors A and B both have positive y-components, and make angles of a = 44.4° and ß = 27.2° with the %3D positive and negative x-axis, respectively. If the vector sum A + B + C = 0, what are the magnitudes of A and B? a |A| = m I |B| = m Figure is not to scale TOOLS x10'Part A Determine the magnitude of the sum of the three vectors V⃗1=6.0i^−9.0j^, V⃗2=i^+j^, and V⃗3=−2.0i^+5.0j^ Express your answer using two significant figures. Part B Determine the angle (in degrees) of the sum of the three vectors V⃗1=6.0i^−9.0j^, V⃗2=i^+j^, and V⃗3=−2.0i^+5.0j^ Express your answer using two significant figures. Part D Determine the angle (in degrees) of V⃗1−V⃗2+V⃗3 Express your answer using two significant figures. Part C Determine the magnitude of V⃗1−V⃗2+V⃗3 Express your answer using two significant figures.
- 1.5 Scalars and Vectors A vector has magnitude 12.7. Rounding off, which pair of components could not produce this vector? O 10.2, 5.5 O 9.6, 8.3 O 12.2, 3.5 O 6.3, 11.0 O 7.1, 10.5 Save for Later Subr Cal_Fall.pdf X PA 20.0° SALA +y C 160 60.0⁰ (a) Number i B (b) Number i The three displacement vectors in the drawing have magnitudes of A = 5.98 m, B = 6.75 m, and C = 4.20 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis which is less than 90°. +x Units UnitsProblem 8: Consider two vectors A and B, expressed in unit vector notation as A= aji+ azj and B = bji+ bzj. A. Part (a) Enter an expression for the vector sum A + B in terms of quantities shown in the expressions above. A+B = B 7 8 HOME a i j k 4 5 6 a1 a2 bị 1 2 3 b2 d + END - h VO BACKSPACE CLEAR m DEL Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. Part (b) Enter an expression for the difference vector A - B in terms of quantities shown in the expressions above. Part (c) Enter an expression for the square of the magnitude of the sum vector |A + B| in terms of quantities shown in the expressions above.