linear algebra Let v1 vk be the points in R3 and suppose th

linear algebra

Let v1, ... v_k be the points in R^3 and suppose that for j = 1, ...k an object with mass v_j is located at point V_j. Physicists call such objects point masses. The total mass of the system of point masses is m = m_1 + ... + m_k. The center of gravity (or center of mass) of the system is v = 1/m [m_1 v_1 +...+m_k v_k] Compute the center of gravity of the system consisting of the point masses above. The center of gravity is at v = (Simplify your answers. Type an ordered triple.)

Solution

v(bar) = (m1v1 +m2v2 +m3v3....)/(m1+m2+m3 ..... mk)

vx = (3*2 +6*5 -4*2 -7*1)/(10) = 2.1

vy = ( -6*2 + 2*5 -2*2 +7*1)/(10) =0.1

vz = ( 4*2 -4*5 -3*3 +4*1)/10 = -1.7

V(ba) = ( 2.1 , 0.1 ,-1.7)