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Snezhnost [94]
3 years ago
5

Use the alternative form of the dot product to find u · v.

Mathematics
1 answer:
vodka [1.7K]3 years ago
7 0

Answer:

Step-by-step explanation:

u = 45

v = 30

Angle between them, θ = 5π / 6 = 150°

(a) The formula for the dot product is given by

\overrightarrow{u}.\overrightarrow{v}= u v Cos\theta

\overrightarrow{u}.\overrightarrow{v}= 45 \times 30 \times Cos150

\overrightarrow{u}.\overrightarrow{v}= -1169.13

(b) \overrightarrow{u}=Cos\frac{\pi }{3}\widehat{i}+Sin\frac{\pi }{3}\widehat{j}

\overrightarrow{u}=0.5\widehat{i}+0.866\widehat{j}

\overrightarrow{v}=Cos\frac{2\pi }{3}\widehat{i}+Sin\frac{2\pi }{3}\widehat{j}

\overrightarrow{v}=-0.707\widehat{i}+0.707\widehat{j}

Let the angle between them is θ

The formula in terms of the dot product is given by

Cos\theta =\frac{\overrightarrow{u}.\overrightarrow{v}}{u v}

u=\sqrt{0.5^{2}+0.866^{2}}=1

v=\sqrt{-0.707^{2}+0.707^{2}}=1

Cos\theta =\frac{0.5 \times (-0.707) + 0.866 \times 0.707)}{1\times 1}

Cos\theta=0.2587

θ = 75°

(c) \overrightarrow{u}=1\widehat{i}+4\widehat{j}+8\widehat{k}

u=\sqrt{1^{2}+4^{2}+8^{2}}=9

Cos\alpha =\frac{1}{9}

Cos\beta =\frac{4}{9}

Cos\gamma  =\frac{8}{9}

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Question 19 (5 points) ✔ Saved
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The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

According to the statement

we have given that the some values of the temperatures and we have to write it in the order from the coolest to the warmest means in increasing order.

So, For this purpose,

The given values of temperatures are:

3°C , -7°C , 2°F, 262 K

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The order of temperature values become -16.7°C > -11.15°C > -7°C > 3°C And -16.7°C is the coolest temperature and 3°C is the warmest as compare to others.

Learn about the increasing order here

brainly.com/question/14662181

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