Express the force F as Cartesian vector form. ✓ Fx • Fy ✓ Fz 150 N 40
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- Consider a vector a = N i=1 ₁a¡ê; expressed in an orthonormal basis. Which of the following statements are true? Negative marking applies. Select one or more: a. (aa) = ₁ ai N i=1 b. (ala) (a|a) = 0 N (a|a) = Σ;₁a;ªz •j=1 □ d. e. f. = (ala) = (aa) = g. (aa) = 1 N ₁a²/ N i=1 * ₁ ažai ₁|a₁|² NA force is specified by the vector F = [(100)i + (-110)j + (70)k] N. Calculate the angles made by F with the positive x-, y-, and z-axes. Answers: ex= i 0 0y = i 0₂ = i OConsidering two force vectors F1 =F1i+F1j+F1k and F2 = F2i+ F»j+F2k with their unit vectors ui = F1 /Fi= (ux)i+ (uiy) j+ (u12) k and u2 = F2 / F2= (u2) i+ (uz)j+ (u2:), which of following are valid calculations for the resultant force FR = F1 + F2? (circle all correct responses) FR = (Fix+ F2x)i+(Fty+F2»)j+ (F1z+ F2)k b. FR = (F: + F2) [(uix+ uzx)i+ (uly+uz)j+ (u1z + u2:2) k] c. FR = (F? + F?)05 [(u1x+ uz)i+ (u¡y + uz) j+ (uiz + uz:) k] d. FR = (F1uix +F2uz)i+(F1u1y+F2u2)j+ (F1u1: +F2u2)k а. %3D %3D с. %3D %3D Consider two vectors A and B with unit vectors u = A/ A and ug = B / B and angle between A and B is 0. Which of the following are correct with regard to dot products? (circle all correct responses) а. A·B is a scalar b. A-B is a vector c. If A and B are parallel, then the magnitude of A·B is the product A*B d. If A and B are perpendicular, then A B = 0 с. е. UA'UB = cos0 Considering springs, cables, and pulleys, which of the following are correct statements? (select all correct…
- Let the x-, y-, and z-axes be identified as axes 1, 2, and 3, respectively. Find the angle between A and axis 2 if A=0.17, Ay = 2.76, and A₂ = 2.98. [Hint: Write the unit vector in the direction of axis 2 and use A. B = A₂ B₂ + A, B, + A₂B₂ = AB cos 1 Φ Record your numerical answer below, assuming three significant figures. AVector A = 2 +33 and vector B = 51-43 +3k. Part A What is the cross product Ax B? Find the -component. Express your answer as integer ► View Available Hint(s) A × B]x = Submit Part B IVE ΑΣΦ α B Y V Ax By = A Submit T P Σ Previous Answers Φ Ψ Ω Find the y-component. Express your answer as integer ▸ View Available Hint(s) € n 6 T φ - ΑΣΦ ħ 0 χ E • * Incorrect; Try Again: 5 attempts remaining A component of a cross product does not equal the product of the respective vector components. You may need to review The Vector Cross Product. You may want to review Hint 1. How to approach the problem. K y @ 2 μ ? ?Given the vectors and w W +(0,0) a) Sketch the vector 3w 6 5 4 3 V 29 ~20 W ننا -2 -3. -4 -5 -6. Clear All Draw: c) Sketch u-u using the Triangle Rule, then sketch the equivalent position vector 6 W 5 43 v2 -6-5-4-3-2-1₁. 1 2 3 4 5 6-6-5 -4 -3 -2 -1₂- -2- -3- -4- -5 -6- Clear All Draw: my s -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 1 2 3 4 5 6 b) Sketch + using the Triangle Rule Ú Clear All Draw: 29 V W 3654 3- بنا يا بلے 1 2 3 4 5 6