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viva [34]
3 years ago
8

Find two unit vectors orthogonal to a=⟨−2,−4,−2⟩a=⟨−2,−4,−2⟩ and b=⟨−3,5,2⟩b=⟨−3,5,2⟩ Enter your answer so that the first non-ze

ro coordinate of the first vector is positive. First Vector: ⟨⟨ , , ⟩⟩ Second Vector: ⟨⟨ , , ⟩⟩ Note: You can earn partial credit on this problem.
Mathematics
1 answer:
Levart [38]3 years ago
7 0

Answer:

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

Step-by-step explanation:

for  a=⟨−2,−4,−2⟩ and b=⟨−3,5,2⟩

a vector orthogonal to a and b can be found through the vectorial product of a and b. Thus

c= a x bc=\left[\begin{array}{ccc}i&j&k\\-2&-4&-2\\-3&5&2\end{array}\right] =  \left[\begin{array}{ccc}-4&-2\\5&2\end{array}\right]*i+\left[\begin{array}{ccc}-2&-2\\-3&2\end{array}\right]*j+\left[\begin{array}{ccc}-2&-4\\-3&5\end{array}\right]*k = 2*i  -10*j  - 22*k

then c₁=⟨2,−10,−22⟩ and c₂= - c₁= ⟨-2,10,22⟩ are orthogonal to a and b

the corresponding unit vectors are

u₁=c₁/|c₁| = ⟨2,−10,−22⟩ / √(2²+(−10)²+(−22)²) = ⟨2,−10,−22⟩/(14*√3) =  ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

then u₂= - u₁=  ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

then the unit vectors are

u₁= ⟨1/(7*√3),−5/(7*√3) ,−11/(7*√3)⟩

u₂= ⟨-1/(7*√3),5/(7*√3) ,11/(7*√3)⟩

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Complete Question:

To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².

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To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more

Step-by-step explanation:

Mass of burlap sacks that Maryann collects = 6 kg

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Area Density = Mass / Area........(1)

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0.4 = Mass / 24

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The mass of burlap used to make Maryann's bulletin board alone:

0.4 = Mass/6

Mass = 2.4 kg

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Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose car was driven x miles in its 4 days trip.

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As per question, total rent is 180 $

Total rent will be = 120 + 0.15 x = 180

Subtracting 120 in both sides

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Here's the solution,

The given triangle is a <em><u>Right</u></em><em><u> </u></em><em><u>angled</u></em><em><u> </u></em><em><u>triangle</u></em><em><u>,</u></em>

So, by applying <em><u>Pythagoras</u></em><em><u> </u></em><em><u>theorem</u></em><em><u>:</u></em>

=》

{c}^{2}  =  {4}^{2}  + 3 {}^{2}

=》

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=》

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6 0
3 years ago
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