The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).

A displacement vector r→ in the xy plane is 49.0 m long and directed at angle θ = 28.0°. Determine (a) the x component and (b) the y component of the vector.

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…

Vector A→, which is directed along an x axis, is to be added to vector B→, which has a magnitude of 9.30 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 5.10 times that of A→. What is the magnitude of A→?