The vectors  are such that a:The  angle between the two vectors is from Physics Motion in A Plane Class 11 Manipur Board
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Motion in A Plane

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Physics Part I

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Physics

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The vectors bold A with bold rightwards arrow on top space and space bold B with bold rightwards arrow on top are such that a:
open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals space open vertical bar straight A with rightwards arrow on top space minus space straight B with rightwards arrow on top close vertical bar
The  angle between the two vectors is

  • 90 degree
  • 60 degree
  • 75 degree
  • 45 degree

A.

90 degree

As we have given
        open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals open vertical bar straight A with rightwards arrow on top minus straight B with rightwards arrow on top close vertical bar
or space space space square root of straight A squared plus straight B squared plus 2 AB space Cosθ end root
space equals square root of straight A squared plus straight B squared minus 2 AB space Cos space straight theta end root
where straight theta is the angle between straight A with rightwards arrow on top space and space straight B with rightwards arrow on top
Squaring both sides, we have
straight A squared plus straight B squared plus 2 AB space Cosθ space equals space straight A squared plus straight B squared minus 2 AB space cosθ
or space space space space space space space space space space space space space space space space space space 4 AB space cosθ space equals space 0
As space space space space space space space space space space space space space space space space space AB not equal to 0
therefore space space space space space space space space space space cosθ space equals space 0 space equals space cos space 90 degree
therefore space space space space space space space space space space space space space space space space space space space space space space space straight theta space equals space 90 degree space space space space space space space space space space space space

Hence, angle between stack straight A space with rightwards arrow on top and space straight B with rightwards arrow on top space is space 90 degree

As we have given
        open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals open vertical bar straight A with rightwards arrow on top minus straight B with rightwards arrow on top close vertical bar
or space space space square root of straight A squared plus straight B squared plus 2 AB space Cosθ end root
space equals square root of straight A squared plus straight B squared minus 2 AB space Cos space straight theta end root
where straight theta is the angle between straight A with rightwards arrow on top space and space straight B with rightwards arrow on top
Squaring both sides, we have
straight A squared plus straight B squared plus 2 AB space Cosθ space equals space straight A squared plus straight B squared minus 2 AB space cosθ
or space space space space space space space space space space space space space space space space space space 4 AB space cosθ space equals space 0
As space space space space space space space space space space space space space space space space space AB not equal to 0
therefore space space space space space space space space space space cosθ space equals space 0 space equals space cos space 90 degree
therefore space space space space space space space space space space space space space space space space space space space space space space space straight theta space equals space 90 degree space space space space space space space space space space space space

Hence, angle between stack straight A space with rightwards arrow on top and space straight B with rightwards arrow on top space is space 90 degree

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