Chapter 1: Q21CP (page 40)

Write the vector $\overset{⇀}{a} = <400, 200, - 100>$ m/s² as the product $|\overset{⇀}{a}| - \overset{⇀}{a}$ .

Short Answer

Expert verified

The required product is $|\overset{⇀}{a}| = \overset{⇀}{a} = (100 \sqrt{21}) <\frac{4}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{1}{\sqrt{21}}>$ .

Step by step solution

Step 1: Definition of the magnitude of a vector

The magnitude of a vectorhaving 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, which is given by:

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

Calculation of magnitude of the vector

Substitute $x = 400, y = 200 a n d z = 100$ into the formula of magnitude to get the magnitude of the vector .

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

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:

$\overset{⇀}{a} = \frac{<400, 200, - 100>}{100 \sqrt{21}} = <\frac{4}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{1}{\sqrt{21}}>$

Calculating the Product of magnitude and the unit vector

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

$|\overset{⇀}{a}| = \overset{⇀}{a} = (100 \sqrt{21}) <\frac{4}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{1}{\sqrt{21}}>$

Thus, the answer $|\overset{⇀}{a}| - \overset{⇀}{a} i s (100 \sqrt{21}) <\frac{4}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{1}{\sqrt{21}}>$ .

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Write the vector $\overset{⇀}{a} = <400, 200, - 100>$ m/s² as the product $|\overset{⇀}{a}| - \overset{⇀}{a}$ .

Short Answer

Step by step solution

Step 1: Definition of the magnitude of a vector

Calculation of magnitude of the vector

Calculating unit vector

Calculating the Product of magnitude and the unit vector

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Write the vector a⇀=400,200,-100m/s2 as the product a⇀-a⇀.

Short Answer

Step by step solution

Step 1: Definition of the magnitude of a vector

Calculation of magnitude of the vector

Calculating unit vector

Calculating the Product of magnitude and the unit vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Further Mechanics and Thermal Physics

Wave Optics

Classical Mechanics

Translational Dynamics

Electricity

Study anywhere. Anytime. Across all devices.

Write the vector $\overset{⇀}{a} = <400, 200, - 100>$ m/s² as the product $|\overset{⇀}{a}| - \overset{⇀}{a}$ .