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Triss [41]
3 years ago
7

If a=i+7j+k and b=i+11j+k, find a unit vector with positive first coordinate orthogonal to both a and

Mathematics
1 answer:
Scilla [17]3 years ago
5 0
Take the cross product, then normalize the result.

\mathbf a\times\mathbf b=\begin{vmatrix}\mathbf i&\mathbf j&\mathbf k\\1&7&1\\1&11&1\end{vmatrix}=-4\,\mathbf i+4\,\mathbf k

This has norm

\|\mathbf a\times\mathbf b\|=\sqrt{(-4)^2+4^2}=4\sqrt2

and so a unit vector orthogonal to both given vectors is

\dfrac{\mathbf a\times\mathbf b}{\|\mathbf a\times\mathbf b\|}=-\dfrac1{\sqrt2}\,\mathbf i+\dfrac1{\sqrt2}\,\mathbf k

An equally correct answer would be the negative of this vector, since \mathbf b\times\mathbf a=-\mathbf a\times\mathbf b.
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X=weekly allowance
x/2=money saved  (=  money spent).
We can suggest this equation:

x/2+4=12

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Answer: her weekly allowance is $16.
7 0
2 years ago
Look at the figure shown below​
Setler79 [48]

Answer:

<em>Answer is </em><em>given below with explanations</em><em>.</em>

Step-by-step explanation:

Answer is option 1) 85 : 51

given \: that \:  \\ triangle \: SPT \: is \: similar \: to \: triangle \:  QPR \\ corresponding \: sides \: of \: similar \:  \\ triangles \: are \: in \: proportion \\ then \:  \\  \frac{SP}{ QP}  =  \frac{PT }{ PR}  \\  \frac{3x}{3x + 24}  =  \frac{51}{85}  \\ taking \: reciprocal \: on \: both \: sides \\  \frac{3x + 24}{3x}  =  \frac{85}{51}

Option 1 is correct.

<em>HAVE A NICE DAY</em><em>!</em>

<em>THANKS FOR GIVING ME THE OPPORTUNITY</em><em> </em><em>TO ANSWER YOUR QUESTION</em><em>. </em>

6 0
3 years ago
Which expression represents 4 more than 2 times the value of n?
Bogdan [553]
2n+4
I really Hope it helps
7 0
3 years ago
The smallest bone on the body, the stirrup-shaped stapes found in the middle ear, has a typical length of less than 0.33 cm. how
4vir4ik [10]

Answer:

0.13 inches.

Step-by-step explanation:

1 inch = 2.54 cm

So 1 cm = 1/ 2.54 in

0.33 cm = 0.33/2.54 in

= 0.13 inches.

5 0
1 year ago
a child should no longer play in the kid zone area when they reach 4'4" tall joe is 54" tall is he allowed to play in the kid zo
Andreyy89

Answer: No.

Step-by-step explanation: Joe is 4'6" tall. Convert 54" to feet by dividing by 12. 54/12=4.5. Half of a foot is 6 inches.

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3 years ago
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