Question

What is the magnitude of the vector $\stackrel{\rightharpoonup }{v}$, where ?

Short answer

The magnitude of the given vector is 21.54$\times$10⁶ m/s .

Step-by-step solution

Given information

The given vector is,

Formula of the magnitude of a vector

The magnitude of a vector$\stackrel{\rightharpoonup }{a}$having coordinatesis given by, $\left|\stackrel{\rightharpoonup }{a}\right|=\sqrt{x^2+y^2+z^2.}$

The magnitude of a vector gives the length of the vector, somagnitude is used to find the length of a vector between the initial and the final point of the vector.

Calculation of the magnitude

Substitute $\left(8\times {10}^6\right)m/s$ for x, 0m/s for y,and $\left(-2\times {10}^7\right)m/s$for zinto the formula of magnitude to get the magnitude of the given vector.

$$\begin{gathered} \left|\stackrel{\rightharpoonup }{v}\right|=\sqrt{{\left(8\times {10}^6\right)}^2+0^2+{\left(-2\times {10}^7\right)}^2}m/s \\ =\sqrt{\left(64\times {10}^{12}\right)+0+\left(4\times {10}^{14}\right)}m/s \\ =\sqrt{464\times {10}^{12}}m/s \\ =21.54\times {10}^{6}m/s \end{gathered}$$

Thus, the magnitude of the given vector $\stackrel{\rightharpoonup }{v}$ is$21.54\times {10}^{6}m/s.$