RESOLVE

Provide full solutions with all math steps shown. . Given the vector @ = 3 +49 _ find the magnitude and direction (angle with respect to the positive x-axis) of @. .Avector 6 has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. Find the x and y components of b. . Find the unit vector in the direction of # = 24 j + 3k. _ A particle's position vector is given by F(t) = (27 t)t + (+5)7 (3t)k Find the particle's velocity vector @() and acceleration vector a(t) as functions of time. . Given = 5a 25 + k, find the direction cosines for this vector. . Integrate the following vector function with respect to time: [ei Atj + 2h)dt. lf @=2ij and b= 31+27, find 24-38. _ A force vector is given by F(t) = (3cos(t))i (2sin(t))j . Determine the change in this force vector between t=O and t= 2: . A particle starts at rest at the origin. It has a constant acceleration of @ = 2i -j (m/s2). We'll soon see that to find its change in velocity vector during some time interval, we need to integrate acceleration over that interval. Please find the change in velocity between t=0 and t. . Identify and describe what is wrong with the following equation and provide a corrected version (if applicable, or explain why no correction is . . 9 ; . . , possible): v= = where # is velocity and @ is acceleration. =