3 years ago

Solve for x. 5x – 14 = 8x + 4 10/3 6 - 10/3 -6 9

Mathematics

1 answer:

amid [387]3 years ago

3 0

Answer:

x = -6

Step-by-step explanation: I hope I helped! :)

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The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .

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3 years ago

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What we want to do first is isolate the variable. To do this we need to multiply each side by 5 to remove the fraction

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