Simplify the expression. Write the answer using scientific notation. 0.3(8.2 x 10^-3)

Mathematics

1 answer:

olchik [2.2K]3 years ago

8 0

Answer:

0.3(8.2 x 10^-3) = 2.46 X 10 ^ -3

Step-by-step explanation:

We need to solve the equation 0.3(8.2 x 10^-3) and write answer in scientific notation.

Solving,

= 0.3(8.2 x 10^-3)

= 0.3 * 0.0082

= 0.00246

Writing in scientific notation

= 2.46 X 10 ^ -3

So, after solving the expression 0.3(8.2 x 10^-3) the result is 2.46 X 10 ^ -3.

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Find two unit vectors orthogonal to both given vectors. i j k, 4i k

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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 $-\mathbf v$ .