Chapter 1: Q21P (page 40)

Write the vector $\overset{⇀}{a =} <400, 100, - 100> m / s^{2}$ as the product $|\overset{⇀}{a}| . \overset{⇀}{a .}$

Short Answer

Expert verified

The required product is $|\overset{⇀}{a}| . \overset{⇀}{a} = 100 \sqrt{21} <\frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}> .$ .

Step by step solution

Definition of magnitude of a vector

The magnitude of a vector $\overset{⇀}{a}$ having coordinates $<x, y, z>$ is written as: $|\overset{⇀}{a}| = \sqrt{x^{2} + y^{2} + z^{2} .}$

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

$\hat{a} = \frac{\overset{⇀}{a}}{|\overset{⇀}{a}|} .$

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 $\overset{⇀}{a}$ .

$|\overset{⇀}{a}| = \sqrt{400^{2} + 200^{2} + {(- 100)}^{2}} = 100 \sqrt{21}$

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:

$\hat{a} = \frac{<400, 200, - 100>}{100 \sqrt{21}} = <\frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}>$

Calculating Product of magnitude and the unit vector

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

$|\overset{⇀}{a}| . \overset{⇀}{a} = 100 \sqrt{21} <\frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}>$

Thus, the answer of $|\overset{⇀}{a}| . \overset{⇀}{a} i s 100 \sqrt{21} <\frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}, \frac{4}{\sqrt{21}}> .$

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Write the vector $\overset{⇀}{a =} <400, 100, - 100> m / s^{2}$ as the product $|\overset{⇀}{a}| . \overset{⇀}{a .}$

Short Answer

Step by step solution

Definition of magnitude of a vector

Calculation of magnitude of vector

Calculating unit vector

Calculating Product of magnitude and the unit vector

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Write the vector a=⇀400,100,-100m/s2as the product a⇀.a.⇀

Short Answer

Step by step solution

Definition of magnitude of a vector

Calculation of magnitude of vector

Calculating unit vector

Calculating Product of magnitude and the unit vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Conservation of Energy and Momentum

Rotational Dynamics

Nuclear Physics

Radiation

Work Energy and Power

Study anywhere. Anytime. Across all devices.

Write the vector $\overset{⇀}{a =} <400, 100, - 100> m / s^{2}$ as the product $|\overset{⇀}{a}| . \overset{⇀}{a .}$