Q41P Use the definition of scalar pro... [FREE SOLUTION]

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Chapter 3: Q41P (page 59)

Use the definition of scalar product, $^{\overset{鈬赌}{a .} \overset{鈬赌}{b} = a b c o s 胃}$ and the fact that $^{a . b = a_{x} b_{x} + a_{y} b_{y} + a_{z} b_{z}}$ to calculate the angle between two vectors given bylocalid="1654245592038" $^{\overset{鈫�}{a} = 3.00 \hat{i} + 3.00 \hat{j} + 3.00 k}$ and $^{\overset{鈬赌}{b} = 2.00 \hat{i} + 1.00 \hat{j} + 3.00 k}$ .

Short Answer

Expert verified

Angle $(胃)$ between $\overset{鈬赌}{a}$ and $\overset{鈬赌}{b}$ is $22^{掳}$ . $\overset{鈬赌}{a} and \overset{鈬赌}{b}$

Step by step solution

Given

$\overset{鈫�}{a} = 3.0 \hat{i} + 3.0 \hat{j} + 3.0 \hat{k} \overset{鈫�}{b} = 2.0 \hat{i} + 1.0 \hat{j} + 3.0 \hat{k}$

Understanding the concept

As we have given the unit vectors, first we calculate the magnitude for the individual vectors and dot product. Using the formula for dot product we can find the angle between them.

Formula:

The dot product is written as,

$\overset{鈬赌}{a} . \overset{鈬赌}{b} = a b \cos 胃$

The dot product is written as,

$a = \sqrt{{(a_{x})}^{2} + {(a_{y})}^{2}}$

Calculate the angle betweena→=3.00i^+3.00j^+3.00k^andb^=2.00i^+1.00j^+3.00k^

Use equation (ii) to calculate the magnitude of the vectors $^{a a n d b}$ . Therefore,

$|\overset{鈫�}{a}| = \sqrt{3 . 0^{2} + 3 . 0^{2} + 3 . 0^{2}} = 5.2 |\overset{鈫�}{b}| = \sqrt{2 . 0^{2} + 1 . 0^{2} + 3 . 0^{2}} = 3.74$

The magnitude of the dot product is calculated as,

$|\overset{鈫�}{a} . \overset{鈫�}{b}| = (3 脳 2) + (3 脳 1) + (3 脳 3) = 6 + 3 + 9 = 18$

Now, use the equation (i) to find the angle.

$18.0 = 5.2 脳 3.74 脳 \cos 胃 \cos 胃 = \frac{18.0}{19.24} 胃 = \cos^{- 1} (\frac{18.0}{19.448}) 胃 = 22 掳$

So, the angle between the two given vectors is $^{22 掳}$
.

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Short Answer

Step by step solution

Given

Understanding the concept

Calculate the angle betweena→=3.00i^+3.00j^+3.00k^andb^=2.00i^+1.00j^+3.00k^

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91影视

Use the definition of scalar product, a.鈬赌b鈬赌=abcos胃and the fact thata.b=axbx+ayby+azbzto calculate the angle between two vectors given bylocalid="1654245592038" a鈫�=3.00i^+3.00j^+3.00kandb鈬赌=2.00i^+1.00j^+3.00k.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the angle betweena→=3.00i^+3.00j^+3.00k^andb^=2.00i^+1.00j^+3.00k^

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Oscillations

Rotational Dynamics

Translational Dynamics

Quantum Physics

Wave Optics

Study anywhere. Anytime. Across all devices.