Question

If U = I + 3j - 2k and V = 4i - 2j - 4k are vectors, find (2U + V) . ( U - 2V )

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Answer 1

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Answer on Question #46930 – Math – Vector Calculus

Question:

If $U = i + 3j - 2k$ and $V = 4i - 2j - 4k$ are vectors, find $(2U + V) \cdot (U - 2V)$

Solution:

$$\begin{array}{l} \vec{U}(1;3;-2), \vec{V}(4;-2;-4) \\ 2\vec{U} + \vec{V} = (6;4;-8) \\ \vec{U} - 2\vec{V} = (-7;7;6) \\ (2\vec{U} + \vec{V})(\vec{U} - 2\vec{V}) = 6 * (-7) + 4 * 7 - 8 * 6 = -62 \\ \end{array}$$