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Let $\mathbf{v}_{1}, \ldots, \mathbf{v}_{k}$ be points in $\mathbb{R}^{3}$ and suppose that for$j=1, \ldots, k$ an object with mass $m_{j}$ is located at point $\mathbf{v}_{j}$ . Physicists call such objects point masses. The total mass of the system of point masses is$$m=m_{1}+\cdots+m_{k}$$The center of gravity (or center of mass) of the system is$$\overline{\mathbf{v}}=\frac{1}{m}\left[m_{1} \mathbf{v}_{1}+\cdots+m_{k} \mathbf{v}_{k}\right]$$Compute the center of gravity of the system consisting of the following point masses (see the figure):figure can't copy

$( 1.3,0.9,0 )$

Algebra

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okay. And this question, we have to complete the center of gravity center off gravity, gravity off the system, Consistent following point masses. So in the question is even it was 25 minus 43 and masses to Graham and point we do is for three minus two and masses 5 g V three is minus four, minus three minus one. And masses program Okay. And point before is minus 986 and masses, 1 g. Okay, so and the central in the formal of center of gravity is also given is one upon em. And one we one plus and do it too. Plus on em que week. So these are the given in the ocean. So now we have to find the central gravity. Okay, So first we will find on this portion. This was in one upon him. So one upon am it was 21 upon in one place and Douglas entry plus m four. So this will be program now 52 and one, then five, two and one. This will be one upon 10. Okay, Now we have to find this and when we want to do it, okay. And for this when we went in this way, will. So all the same for Eman is too. And we even points are five minus 43 Now I can do it so that I am to his five. And we do is 43 minus two and empty TV three. The empty is do and we tree is minus four, minus three minus one. And am for we for is m four is one and we for is minus 98 and six. Okay. And the resultant will be We have to fight it. Okay, so this will be then minus eight and six on this will be plus 20 plus 15 minus 10 and then minus eight minus six minus two and then minus nine. Plus eight plus six on this will be 13, 9 and zero. Okay, so we have the value. Now we will put these value in the formula. So we central gravity is one upon AM and m one m two plus m m m m money one plus two plus 33 plus emporium. A four is 13, 9 and zero, and that will be 1.30 point nine and zero. That means the central of gravity is 1.30 point nine and zero on. This is our final answer. Thank you.

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