1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
IgorC [24]
3 years ago
13

Given any triangle in the plane, associate to each side an outward pointing normal vector of the same length as the side. Show t

hat the sum of these three vectors is always 0.
Mathematics
1 answer:
Zigmanuir [339]3 years ago
8 0

Let , a, b and c be the length of three sides of triangle, represented in terms of vectors as \vec{a},\vec{b},\vec{c}.

Now, vector of same Magnitude acts as normal vector to each side.

So, equation of any vector p having normal q is given by

      \vec{p} \times\vec{q}

Now sum of three vector and it's normal is given as

    =\vec{a} \times\vec{a}+\vec{b} \times\vec{b}+\vec{c} \times\vec{c}\\\\=0+0+0\\\\=0

Cross product of two identical vectors is Zero.

\rightarrow \vec{i} \times\vec{i}=0

You might be interested in
A cube has a volume of 64. What is the length of one side of the cube?
bearhunter [10]

Answer:

4

Step-by-step explanation:

The volume of a cube can be represented as s^3 = v, where s = side and v = volume. In this case, we're given the volume as 64, so s^3 = 64. To solve this problem, we first have to know what a cube root is.

What's a cube root?

  • The cube root of a number is the number you multiply by itself 3 times to get another number.
  • One common cube is 27, and the cube root of it is 3 because 3 x 3 x 3 = 27.

Given the information above, let's go in order with the list of cube roots to see which one has a cube of 64.

  • 1: 1 x 1 x 1 = 1.
  • 2: 2 x 2 x 2 = 8.
  • 3: 3 x 3 x 3 = 27.
  • 4: 4 x 4 x 4 = 64. (This is the cube root!)

We found the cube root of 64, or the side of the cube with a volume of 64. The side of the cube, therefore, is 4.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

3 0
2 years ago
Xft
salantis [7]

Answer:

640.0

Step-by-step explanation:

7 0
3 years ago
Help me out please simple
const2013 [10]

<u>A straight line is 180 degrees in measure</u>

<u>The straight line is made up of three angles</u>

           --> angle 1

           --> angle 2

           --> angle with a little square on it

                     (<em>angle with a little square means it is 90 degrees in measure)</em>

<u>Let's set up an equation</u>

    angle1 + angle2 + 90 = 180\\angle1 + 87 + 90 = 180\\angle1 = 3

Thus angle 1 is <u>3 degrees</u> or the <u>second choice</u>

<u></u>

Hope that helps!

5 0
3 years ago
Find the point on the line 2x+4y−3=0 which is closest to the point (2,0)
Finger [1]
L1: 2x+4y-3=0 ..........(1)
P: (2,0)
The point on the line L1 closest to the given point P is at the intersection of L1 with L2, which is the perpendicular passing through P. 

Slope of L1=-2/4=-1/2
Slope of L2=-1/(-1/2)=2
Since it passes throug P(2,0), we can use the point-slope formula:
(y-0)=2(x-2)  =>
L2: 2x-y-4=0.............(2)

Solve for x & y using (1) and (2) to get intersection point required:
(1)-(2)
2x-2x + 4y-(-y) -3 -(-4) =0
5y=-1, y=-1/5
Substitute y=1/5 in equation (1)
2x+4(-1/5)-3=0 =>
2x-19/5=0
x=19/10

=> the point on L1 closest to (2,0) is (19/10, -1/5)

7 0
3 years ago
when they said went to bed the outside temperature was 28 degrees Fahrenheit when you woke up the next morning the temperature h
Ghella [55]

Answer:

41 degrees

Step-by-step explanation:

just subtract

7 0
3 years ago
Other questions:
  • Russia covers about 1/30 of the earth surface. The area of Russia is about 1 2/3 times the area of Canada. What fraction of the
    5·1 answer
  • Alexander purchased a computer on sale. The regional price was $1200. The sale price was 5/6 of the original price. How much did
    7·1 answer
  • In Spencer’s garden, the number of rose bushes is 7 less than 1.5 times the number of carnation bushes. If the number of carnati
    14·2 answers
  • A board is 12 feet long. If the board is divided into 12 equal sections, how long is each section?
    7·1 answer
  • Use the system of equations. Please show your steps and how you solved it!
    5·1 answer
  • What is the answer to -3x+2=-7
    10·2 answers
  • What is An equivalent fraction to 1/2 with a denominator as 10?
    9·2 answers
  • What is the initial value of the function represented by this table?
    8·1 answer
  • 50% of the tickets sold at a water park were child tickets. If the park sold 44 tickets in all, how many child tickets did it se
    15·2 answers
  • If L = 7 inches, W = 5 inches, and H = 3 inches, what is the volume of the rectangular prism?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!