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what is the dot product and cross product of of two vectors if the angle is between them is 90 degree?

DaniilM [7]

$\sf{\pink{\underline{\underline{\blue{GIVEN:-}}}}}$

The angle between the two vectors is 90° .

$\sf{\pink{\underline{\underline{\blue{TO\: FIND:-}}}}}$

The dot product of two vectors .
The cross product of two vectors .

$\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}$

⚡ Let $\rm{\vec{a}}$ and $\rm{\vec{b}}$ are the two vectors .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:ab\cos{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\cos{90^{\degree}}\:}$

cos 90° = <u>0</u>

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\times{0}\:}$

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:0\:}$

$\rm{\red{\therefore}}$ [1] The dot product of two vectors is “ <u>0</u> ” .

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:\times\:\vec{b}\:=\:ab\sin{\theta}\:}}}}$

Where,

θ = 90°

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\sin{90^{\degree}}\:}$

sin 90° = <u>1</u>

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\times{1}\:}$

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\:}$

$\rm{\red{\therefore}}$ [2] The cross product of two vectors is “ <u>ab</u> ” .

3 0

3 years ago

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The force of attraction between a -165.0 uC and +115.0 C charge is 6.00 N. What is the separation between these two charges in m

Simora [160]

Answer:

The distance between the charges is 5,335.026 m

Explanation:

To obtain the forces between the particles, we can use Coulomb's Law in scalar form, this is, the force between the particles will be:

$F = k \frac{q_1 q_2}{d^2}$

where k is Coulomb's constant, $q_1$ and $q_2$ are the charges and d is the distance between the charges.

Working a little the equation, we can take:

$d^2 = k \frac{q_1 q_2}{F}$

$d = \sqrt{ k \frac{q_1 q_2}{F}}$

And this equation will give us the distance between the charges. Taking the values of the problem

$k= 9.00 \ 10^9 \frac{N \ m^2}{C^2} \\q_1 = 165.0 \mu C \\q_2 = 115.0 C\\F=- 6.00$

(the force has a minus sign, as its attractive)

$d = \sqrt{ 9.00 \ 10^9 \frac{N \ m^2}{C^2} \frac{(165.0 \mu C) (115.0 C)}{- 6.00 \ N}}$

$d = \sqrt{ 28,462,500 \ m^2}}$

$d = 5,335.026 m$

And this is the distance between the charges.

3 0

3 years ago

Three observers watch a train pull away from a station toward the right of the platform. Observer A is in one of the train’s car

juin [17]

Observer A is moving inside the train

so here observer A will not be able to see the change in position of train as he is standing in the same reference frame

So here as per observer A the train will remain at rest and its not moving at all

Observer B is standing on the platform so here it is a stationary reference frame which is outside the moving body

So here observer B will see the actual motion of train which is moving in forward direction away from the platform

Observer C is inside other train which is moving in opposite direction on parallel track. So as per observer C the train is coming nearer to him at faster speed then the actual speed because they are moving in opposite direction

So the distance between them will decrease at faster rate

Now as per Newton's II law

F = ma

Now if train apply the brakes the net force on it will be opposite to its motion

So we can say

- F = ma

$a = \frac{-F}{m}$

so here acceleration negative will show that train will get slower and its distance with respect to us is now increasing with less rate

It is not affected by the gravity because the gravity will cause the weight of train and this weight is always counterbalanced by normal force on the train

So there is no effect on train motion

5 0

3 years ago

A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother’s mass is exactly twi

a_sh-v [17]

The sister suddenly pushes her brother. As a result, the sister moves with kinetic energy k. The resulting kinetic energy of the brother is k/2.

<h3>What is kinetic energy?</h3>

The ability of an object to do work by virtue of its motion is called the kinetic energy.

A brother and sister are standing next to each other at rest on a surface of frictionless ice. The brother’s mass is exactly twice that of his sister’s.

If the sister's mass is m, the brother's mass is 2m.

The kinetic energy of sister is k =1/2 mv²,

The velocity will also get halved for brother, So, the kinetic energy of brother will be

k' = 1/2 (2m)(v/2)²

On comparing, the relation between the kinetic energy of brother and sister is k' = k/2

Thus, the resulting kinetic energy of the brother is k/2.

Learn more about kinetic energy.

brainly.com/question/12669551

#SPJ4

7 0

1 year ago

How is the acceleration of an object in newtons second law related to its mass and the net force on it?

9966 [12]

B) Acceleration is directly proportional to the mass of the object

4 0

3 years ago

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