1. Determine the unit vector o in the direction frompointc touaids pointD. (which is the/ direction of the force Fof the figue. 2. Determine the menment Mo of h the force F about the point De
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Express each result of Parts 1-5 in the form of a Cartesian vector. Part 4 requires the specification of 2 cartesian vectors: a force and a moment vector.
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- The figure shows two vectors, A and B, whose magnitudes are A = 6.8 and B = 5.5.Consider the following vectors: A = 1.2i + 4.9j + 3.7k B = -8.5i + 7.5j + 8.3k Part (a) What is the x-component of the vector V = 3(A × 2B)? Part (b) What is the y-component of the vector V = 3(A × 2B)? Part (c) What is the z-component of the vector V = 3(A × 2B)? Part (d) What is the magnitude of the vector V?Calculate the magnitude
- We have two vectors A=(6.0, 9.6) and B=(-8.6, 4.4). What angle does the sum of these vectors make with the x-axis in degrees?Considering 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…A vector a of magnitude 17 units and another vector b of magnitude 8.5 units differ in directions by 72°. Find (a) the scalar product of the two vectors and (b) the magnitude of the vector product a×b.
- The cross product AxB is perpendicular to both vectors in the cross product (think of Aand В as lying on a sheet of paper; the cross product is perpendicular to the plane of the sheet). After figuring out the two directions perpendicular to both vectors you use one of the right hand rules given on Page 338 to choose which of the two direction is correct. All three should give the same result so use whichever one you are most comfortable with. In class, we will use the middle one in the diagram in the book. The vector torque is where "is the vector from the axis of rotation to where the force is applied. Which is the direction of the torque vector? +y ++ * (in) +z (out) O = in (O) = outGiven the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following. (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.) ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.) ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.) °Problem 9.35 - Enhanced - with Expanded Hints An 8.5 kg crate is pulled 5.1 m up a 30° incline by a rope angled 16° above the incline. The tension in the rope is 140 N and the crate's coefficient of kinetic friction on the incline is 0.25. For help with math skills, you may want to review: The Vector Dot Product ▼ SOLVE: Part B WT = T·Ar=TAx cos(16) = (140 N) (5.1 m) cos(16) = 690 J WG = FG Ar = mg▲x cos(120°) = (8.5 kg) (9.8 m/s²)(5.1 m) cos(120°) Wn=n· Ar=nAx cos(90°) = 0 J What is the increase in thermal energy of the crate and incline? Express your answer in joules to two significant figures. ► View Available Hint(s) VE ΑΣΦ ΔΕth = |105 Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining ? 10 of 14 J Re
- What is the relation between A×B and BxA, The magnitudes are the same but they are in opposite directions, i.e., (Ã×B)=-(BxÃ) The order of the vectors in a cross product doesn't matter so they are the same, i.e., (ÃxB)=(BxÃ)Consider the vectors A=<1,2,3>, B=<-2,1,0>, and C=<0,3,1>. (a)Find the angle between A and B. (b)Find the component of A in the direction of C.