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Addition of Vectors

The sides of ...

Question

The sides of a parallelogram are $2^i + 4^j - 5^k$ and $^i + 2^j + 3^k$ . Find the unit vector parallel to the diagonals.

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Solution

$\begin{matrix} D i a g o n a l s o f ∥ g m a r e (2^i + 4^j - 5^k) + (^i + 2^j + 3^k) \equiv (3, 6, - 2) a n d, (2^i + 4^j -^5) - (^i + 2^j + 3^k) \equiv (1, 2, - 8) U n i t v e c t o r p a r a l l e l t o d i a g o n a l s a r e : \frac{3^i + 6^j - 2^k}{7} = \frac{^i + 2^j - 8^k}{\sqrt{69}} \end{matrix}$

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