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Levart [38]
3 years ago
6

Use vectors to decide whether the triangle with vertices P(1, −2, −1), Q(2, 1, −3), and R(6, −1, −4) is right-angled. Yes, it is

right-angled. No, it is not right-angled.
Physics
1 answer:
Andreas93 [3]3 years ago
3 0

Answer:

Yes, it is right-angled

Explanation:

Two vectors are orthogonal if the scalar product between them is zero. Then, we will match each pair of vertices with a vector, wich is formed with the following formula:

Given two points A and B, the vector going from A to B is

AB=B-A=(B_{x}-A_{x},B_{y}-A_{y},B_{z} -A_{z})

So, we calculate each component separately.

PQ=Q-P=(2-1,1-(-2),-3-(-1))=(1,3,-2)

QR=R-Q=(6-2,-1-1,-4-(-3))=(4,-2,-1)

RP=P-R=(1-6,-2-(-1),-1-(-4))=(-5,-1,3)

Finally, using the scalar product formula

A*B=A_{x}* B_{x}+ A_{y}* B_{y}+ A_{z}* B_{z}

we see if the products is zero

PQ*QR=1*4+3(-2)+(-2)*(-1)=0

In this case we don't even have to calculate the other products as we've found that PQ and QR form a right angle.

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The energy released by the exploding gunpowder in a cannon propels the cannonball forward. Simultaneously, the cannon recoils. T
Lelechka [254]

Answer:

the launched cannonball

Explanation:

4 0
3 years ago
Using Mirror equation A, Calculate The Frequency Of The Long Stand And The Shortest Wave Length Of That An Object Is Placed Of A
Leya [2.2K]

The Image distance and Magnification of The Image ​will be 30 cm and 3.

<h3>What is focal length?</h3>

The focal length of the lens, which is often expressed in millimeters, is the distance between the lens and the image sensor when the subject is in focus.

Given data;

Focal length,f=?

Image distance,v=?

Object distance,u= 10 cm

Magnification,m= 2.85

The focal length is half of the radius;

f=R/2

f=30 Cm/2

f= 15 Cm

The mirror equation is found as;

\rm \frac{1}{f} =\frac{1}{v} +\frac{1}{u} \\\\\ \frac{1}{15}=\frac{1}{v}+\frac{1}{10} }  \\\\\ v= -30 \ cm

The magnification of the lens is found as;

\rm m=\frac{30}{10}\\\\ m=3

Hence, the image distance and magnification of The image ​will be 30 cm and 3.

To learn more about the focal length refer;

brainly.com/question/16188698

#SPJ1

6 0
2 years ago
Consider two diffraction gratings. One grating has 3000 lines per cm, and the other one has 6000 lines per cm. Both gratings are
Usimov [2.4K]

Answer:

<em>The 6000 lines per cm grating, will produces the greater dispersion .</em>

Explanation:

A diffraction grating is an optical component with a periodic (usually one  that has ridges or rulings on their surface rather than dark lines) structure that splits and diffracts light into several beams travelling in different directions.

The directions of the light beam produced from a diffraction grating depend on the spacing of the grating, and also on the wavelength of the light.

For a plane diffraction grating, the angular positions of principle maxima is given by

(a + b) sin ∅n = nλ

where

a+b is the distance between two consecutive slits

n is the order of principal maxima

λ is the wavelength of the light

From the equation, we can see that without sin ∅ exceeding 1, increasing the number of lines per cm will lead to a decrease between the spacing between consecutive slits.

In this case, light of the same wavelength is used. If λ and n is held constant, then we'll see that reducing the distance between two consecutive slits (a + b) will lead to an increase in the angle of dispersion sin ∅. So long as the limit of sin ∅ not greater that one is maintained.

7 0
3 years ago
In Florida, once you have had your learner's license for _________________ without any traffic convictions, you will receive an
bogdanovich [222]

Answer:

One year

Explanation:

In Florida, once you have had your learner's license for 1 year without any traffic convictions, you will receive an intermediate license.

The rule for Florida is that if a driver drives safely without any conviction during that year of his trial, he will receive an intermediate license. This means that he is now completely eligible and safe to drive around Florida's roads.

I hope the answer is helpful.

Thanks for asking.

3 0
3 years ago
Which three statements about electromagnetic radiation are true?
grandymaker [24]
I think that numbers one, three, and four are true
3 0
3 years ago
Read 2 more answers
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