Solve 3D Vector V1-V2+V3 Equations: Find V1,V2,V3 & Magnitude & Direction of V

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The discussion focuses on solving a system of three linear equations involving three-dimensional vectors V1, V2, and V3. The equations are V1–V2 + V3 = 2i + 2j + 3k, V1–2V2-2V3 = -5i + 7j + 8k, and V1 + V2 + V3 = 4i - 2j - k. Participants suggest using substitution and elimination methods to derive the values of V1, V2, and V3, ultimately leading to the calculation of vector V = V1 + V3, including its magnitude and direction.

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V1–V2 +V3 = 2i+2j+3k, V1– 2V2-2V3 = -5i+7j+8k, and V1+V2+V3 = 4i-2j-k

a) Find V1,V2, and V3

b) Find V=V1+V3 in terms of its components. What is the magnitude and direction of V?


All I know is that they are three dimensional vectors.

Any help will be much appreciated
 
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[tex]\vec{V}_{1} = 2\hat{i} + 2\hat{j} + 3\hat{k} + \vec{V}_{2} - \vec{V}_{3}[/tex]
Using substitution you should be able to solve for the 3 vectors.
 
Essentially, you are talking about solving three linear equations for the three unknowns,
V1, V2, and V3. odie5533's suggestion is good. It also appears that if you multiply the equation V1–V2 +V3 = 2i+2j+3k by 2 to get 2V1–2V2 +2V3 = 4i+4j+6k,and add that to the first equation, V1– 2V2-2V3 = -5i+7j+8k, you eliminate V3 from the equations. Treat it exactly like solving simultaneous.
 

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