Chapter 1: Q12P (page 39)

What is the magnitude of the vector $\overset{⇀}{v}$ , where $\overset{⇀}{v} = <8 \times 10^{6}, 0, - 2 \times 10^{7}> m / s$ ?

Short Answer

Expert verified

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

Step by step solution

Given information

The given vector is, $\overset{⇀}{v} = <8 \times 10^{6}, 0, - 2 \times 10^{- 17}> m / s .$

Formula of the magnitude of a vector

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

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

$|\overset{⇀}{v}| = \sqrt{{(8 \times 10^{6})}^{2} + 0^{2} + {(- 2 \times 10^{7})}^{2}} m / s = \sqrt{(64 \times 10^{12}) + 0 + (4 \times 10^{14})} m / s = \sqrt{464 \times 10^{12}} m / s = 21.54 \times 10^{6} m / s$

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

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What is the magnitude of the vector $\overset{⇀}{v}$ , where $\overset{⇀}{v} = <8 \times 10^{6}, 0, - 2 \times 10^{7}> m / s$ ?

Short Answer

Step by step solution

Given information

Formula of the magnitude of a vector

Calculation of the magnitude

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What is the magnitude of the vector v⇀, wherev⇀=8×106,0,-2×107m/s ?

Short Answer

Step by step solution

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Formula of the magnitude of a vector

Calculation of the magnitude

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What is the magnitude of the vector $\overset{⇀}{v}$ , where $\overset{⇀}{v} = <8 \times 10^{6}, 0, - 2 \times 10^{7}> m / s$ ?