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
solniwko [45]
2 years ago
9

If vector A =i+2j-k and vec A cross vec B =3i-j+5k. find vec B​​​

Physics
1 answer:
postnew [5]2 years ago
8 0

Let <em>B</em> = <em>a</em> <em>i</em> + <em>b</em> <em>j</em> + <em>c</em> <em>k</em>. Then the cross product of <em>A</em> = <em>i</em> + 2<em>j</em> - <em>k</em> with <em>B</em> is

<em>A</em> × <em>B</em> = ( <em>i</em> + 2<em>j</em> - <em>k </em>) × ( <em>a</em> <em>i</em> + <em>b</em> <em>j</em> + <em>c</em> <em>k</em> )

<em>A</em> × <em>B</em>  = <em>a</em> ( <em>i</em> × <em>i</em> ) + 2<em>a</em> ( <em>j</em> × <em>i</em> ) - <em>a</em> ( <em>k</em> × <em>i </em>)

… … … + <em>b</em> ( <em>i</em> × <em>j</em> ) + 2<em>b</em> ( <em>j </em>× <em>j</em> ) - <em>b</em> ( <em>k</em> × <em>j</em> )

… … … + <em>c</em> ( <em>i</em> × <em>k</em> ) + 2<em>c</em> ( <em>j</em> × <em>k</em> ) - <em>c</em> ( <em>k</em> × <em>k</em> )

<em>A</em> × <em>B</em> = 0 - 2<em>a</em> <em>k </em>- <em>a</em> <em>j</em>

… … … + <em>b</em> <em>k</em> + 0 + <em>b</em> <em>i</em>

… … … - <em>c</em> <em>j</em> + 2<em>c</em> <em>i</em> - 0

<em>A</em> × <em>B</em> = (<em>b</em> + 2<em>c</em>) <em>i</em> + (-<em>a</em> - <em>c</em>) <em>j</em> + (<em>b</em> - 2<em>a</em>) <em>k</em>

So we have

3 <em>i</em> - <em>j</em> + 5 <em>k </em>= (<em>b</em> + 2<em>c</em>) <em>i</em> + (<em>c</em> - <em>a</em>) <em>j</em> + (<em>b</em> - 2<em>a</em>) <em>k</em>

which gives us the system of equations,

{ <em>b</em> + 2<em>c</em> = 3

{ -<em>a</em> - <em>c</em> = -1

{ -2<em>a</em> + <em>b</em> = 5

Solve for <em>a</em>, <em>b</em>, and <em>c</em>.

• Eliminate <em>c</em> from the first two equations:

(<em>b</em> + 2<em>c</em>) + 2 (-<em>a</em> - <em>c</em>) = 3 + 2 (-1)

-2<em>a</em> + <em>b</em> = 1

But -2<em>a</em> + <em>b</em> = 5, and 5 ≠ 1, so there is no such vector <em>B</em> that satisfies the cross product!

You might be interested in
Conduction is usually faster/slower in liquids and certain solids than in gases.
KIM [24]
Conduction is slower in liquids and gases.

Liquids it is convection which transmits more heat.. quicker...

Materials which are good conductors of thermal energy are called thermal conductors.

metals are good thermal conductors.


6 0
3 years ago
21. If the Sun's rays were at 45° to a vertical pillar, how would
diamong [38]

Answer:

Let the height of the pole AB = x m. ∴ Length of shadow OB ol the pole AB = x m. Let the angle of elevation be ө, i.e. Hence, the angle of elevation of the Sun's altitude is 45°.

Explanation:

4 0
3 years ago
if you knew the number of valence electrons in a nonmetal atom, how would you determine the valence of the element?
Vanyuwa [196]
It would be funny because . I will not be good
8 0
3 years ago
What must happen to an atom of magnesium in order to become a magnesium ion Mg+2?
igomit [66]

Answer:

Answer is: c. It must lose two electrons and become an ion.

Magnesium (Mg) is metal from 2. group of Periodic table of elements and has low ionisation energy and electronegativity, which means it easily lose valence electons (two valence electrons).

Magnesium has atomic number 12, which means it has 12 protons and 12 electrons. It lost two electrons to form magnesium cation (Mg²⁺) with stable electron configuration like closest noble gas neon (Ne) with 10 electrons.

Electron configuration of magnesium ion: ₁₂Mg²⁺ 1s² 2s² 2p⁶.

Explanation:

4 0
3 years ago
Read 2 more answers
The coordinates of a bird flying in the xy-plane are given by x(t)=αt and y(t)=3.0m−βt2, where α=2.4m/s and β=1.2m/s2.part a:Cal
8090 [49]
Α=2.4 \frac{m}{s}

β=1.2 \frac{m}{s^2}

x(t)=at

y(t)=3-βt^2

Vx(t)=α

Vy(t)=-2βt

vectorV=[α;-2βt]

ax(t)=0

ay(t)=-2βt

vector a [0;-2βt]


3 0
3 years ago
Other questions:
  • What's the atom and ion for Calcium
    12·1 answer
  • What is the gravitational force between two identical 5000 kg asteroids whose centers of mass are seperated by 100 m?
    11·1 answer
  • Where are the longest continuous mountain ranges on Earth located?
    10·1 answer
  • This is a map that shows hot spots around the world.
    8·2 answers
  • Water flowing through a watershed is effected greatly by which force?
    5·2 answers
  • Which action will cause the induced current to decrease or remain constant?
    6·1 answer
  • If an object is not accelerating, it can exist in what 2 other states of motion?
    13·1 answer
  • 10
    5·1 answer
  • Forces are _______________ quantities since they have magnitude and direction.
    13·1 answer
  • A 100-m long transmission cable is suspended between two towers. If the mass density is 2. 01 kg/m and the tension in the cable
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!