Physics, asked by sujalsharma10me159, 3 months ago

If |

⃗A⃗ × B⃗ | = |

⃗A⃗ ∙ B⃗ | then angle between ⃗A⃗ and B⃗ is ……​

Answers

Answered by imshilpachauhan
2

Answer:

theta =π/4 or 45°

Explanation:

If we consider θ to be the angle between the vectors A and B,

by defination of cross pr

Therfore, the angle between A and B is π/4 radians.

Answered by pulakmath007
10

SOLUTION

GIVEN

 \sf{  | \: \vec{A} \times  \vec{B} \: |  =  | \:  \vec{A} \:  . \:  \vec{B}\: |  }

TO DETERMINE

 \sf{The \:  angle \:  between \:  \:   \vec{A}  \:  \: and \:  \:   \vec{B}  }

FORMULA TO BE IMPLEMENTED

 \sf{For  \: two  \: vectors \:  \vec{ A} \:  \: and \:  \vec{B}}

 \sf{Let \:   \: \theta \:  \: be \: the \:  angle \:  between \:  \:   \vec{A}  \:  \: and \:  \:   \vec{B}  }

CROSS PRODUCT

 \sf{ \vec{A} \times  \vec{B} =   |\vec{A}| \: |\vec{B} |   \sin \theta  \: \hat{n}}

Where  \sf{ \hat{n}} is a unit vector indicating direction

So that

 \sf{  |\vec{A} \times  \vec{B}|  =   |\vec{A}| \: |\vec{B} |   \sin \theta  \:}

DOT PRODUCT

 \sf{ \vec{A} .  \vec{B} =   |\vec{A}| \: |\vec{B} |   \cos \theta  }

So that

 \sf{  | \vec{A} .  \vec{B}\: |  =   |\vec{A}| \: |\vec{B} |   \cos \theta  }

EVALUATION

Here it is given that

 \sf{  | \: \vec{A} \times  \vec{B} \: |  =  | \:  \vec{A} \:  . \:  \vec{B}\: |  }

 \sf{   \implies \:  \:  |\vec{A}| \: |\vec{B} |   \sin \theta   =  | \vec{A}| \: |\vec{B} |   \cos \theta\:}

 \sf{   \implies \:  \: \sin \theta   =   \cos \theta\:}

 \sf{   \implies \:  \: \tan \theta   =   1\:}

 \displaystyle \sf{   \implies \:  \theta   =    \frac{\pi}{4} \:}

 \displaystyle \:  \sf{ \therefore \:  \: The \:  angle \:  between \:  \:   \vec{A}  \:  \: and \:  \:   \vec{B}  \:  \: is \:  \:  \frac{\pi}{4}  }

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. If c is perpendicular to both a and b, then prove that it is also perpendicular to both a+b and a-b

https://brainly.in/question/22657880

2. If the magnitude of sum of two non zero vectors is equal to the magnitude of their difference then which of the followings

https://brainly.in/question/29779844

Similar questions