Let vk be vectors, and suppose that a point mass of mk is located at the tip of each vector. the center of mass for this set of point masses is equal to: v = [(m1v1 ++ mkvk)/m] where m = m1 ++ mk. determine how to divide a total mass of 11 kg among the vectors u1 = (−1, 3), u2 = (3, −2), and u3 = (5, 2) so that the center of mass is (21/11, 6/11).

m1 = 4

m2 = 5

m3 = 2

Step-by-step explanation:

given (21/11, 6/11) = m1 (-1/3) + m2 (3, -2) + m3 (5, 2)

= (-m1 + 3m2 + 5m3) / 11 = 21/11

= (3m1 + (-2)m2 + 2m3) / 11 = 6/11

so that m1 + m2 +m3 = 11

-m1 + 3m2 + 5m3 = 21

3m1 - 2m2 + 2m3 = 6

from this, we get the augmented matrix as

\left[\begin{array}{cccc}-1&1&1&11\\-1&3&5&21\\3&-2&2&6\end{array}\right]

= \left[\begin{array{cccc}-1&1&1&11\\0&4&6&32\\0&-5&-1&-27\end{array}\right]  \left \{ {{R2=R2 + R1} \atop {R3=R3 -3R1 }]} \right.

= \left[\begin{array}{cccc}-1&1&1&11\\0&1&3/2&8\\0&-5&-1&-27\end{array}\right]

= \left[\begin{array}{cccc}-1&1&1&11\\0&1&3/2&8\\0&0&13/2&13\end{array}\right]

(R3 = R3 + 5R2)

this gives m1 + m2 + m3 = 11

m2 + 3/2 m3 = 8

13/2 m3 = 8

13/2 m3 = 13

m3 = 2

m2 = 8 -3/2 (2) = 5

= m1 = 11- 5 - 2 = 4

this gives

m1 = 4

m2 = 5

m3 = 2

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

chiken

step-by-step explanation: