Question

Write the vector as the product $\left|\stackrel{\rightharpoonup }{a}\right|.\stackrel{\rightharpoonup }{a.}$

Short answer

The required product is .

Step-by-step solution

Definition of magnitude of a vector

The magnitude of a vector $\stackrel{\rightharpoonup }{a}$having coordinates is written as:$\left|\stackrel{\rightharpoonup }{a}\right|=\sqrt{x^2+y^2+z^2.}$

The unit vector in the direction of a vector is the vector divided by its magnitude that is given by:

$\hat{a}=\frac{\stackrel{\rightharpoonup }{a}}{\left|\stackrel{\rightharpoonup }{a}\right|}.$

Calculation of magnitude of vector

Substitute x=400, y=200 and z=-100 into the formula of magnitude to get the magnitude of the vector $\stackrel{\rightharpoonup }{a}$.

$$\begin{gathered} \left|\stackrel{\rightharpoonup }{a}\right|=\sqrt{{400}^2+{200}^2+{\left(-100\right)}^2} \\ =100\sqrt{21} \end{gathered}$$

Calculating unit vector

Divide the given vector by its magnitude to get its unit vector.

The unit vector in the direction of a vector is the vector divided by its magnitude:

Calculating Product of magnitude and the unit vector

Multiply the obtained magnitude by the obtained unit vector to get the required result.

Thus, the answer of