Question

Vector A has a magnitude of 146 units and points 36.0° north of west. Vector B points 63.0° east of north. Vector points 16.0° west of south. These three vectors add to give a resultant vector that is zero. Using components, find the magnitudes of the following vectors e) vector B x units (b) vector C x units Enter a number

Answer 1

$\\a_X=-146\;cos36\\\\ A_y=146\;sin36\\\\ B_x=B\;sin63\\\\ B_y=B\;cos63\\\\ C_x=-C\;sin16\\\\ C_y=-C\;cos16\\\\ given\;resultant\;vector=0\\\\ R_x=0\\\\ A_x + B_x + C_x=0\\\\ -146\;cos36+Bsin63-Csin16=0\\ Csin16=-146\;cos36+B\;sin63...(1)\\\\\\ R_y=0\\\\ A_y + B_y + C_y=0\\\\ 146\;sin36+Bcos63-Ccos16=0\\ Ccos16=146\;sin36+B\;cos63.....(2)\\\\\\from\;(1)\;and\;(2)\\ tan16=\frac{-146\;cos36+B\;sin63}{146\;sin36+B\;cos63}\\\\ B=188\;\\\\ using\;B\;in\;1\\$ $\\a_X=-146\;cos36\\\\ A_y=146\;sin36\\\\ B_x=B\;sin63\\\\ B_y=B\;cos63\\\\ C_x=-C\;sin16\\\\ C_y=-C\;cos16\\\\ given\;resultant\;vector=0\\\\ R_x=0\\\\ A_x + B_x + C_x=0\\\\ -146\;cos36+Bsin63-Csin16=0\\ Csin16=-146\;cos36+B\;sin63...(1)\\\\\\ R_y=0\\\\ A_y + B_y + C_y=0\\\\ 146\;sin36+Bcos63-Ccos16=0\\ Ccos16=146\;sin36+B\;cos63.....(2)\\\\\\from\;(1)\;and\;(2)\\ tan16=\frac{-146\;cos36+B\;sin63}{146\;sin36+B\;cos63}\\\\ B=188\;\\\\$

$\\using\;B\;in\;(1)\\\\ C=179.2$