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Motion In A Plane

Question
CBSEENPH11020783

bold A with bold rightwards arrow on top bold space and bold space bold B with bold rightwards arrow on top are two vectors and θ is the angle between them if vertical line bold A with bold rightwards arrow on top bold space straight x bold space bold B with bold rightwards arrow on top bold vertical line bold space equals bold space square root of bold 3 bold space bold left parenthesis bold A with bold rightwards arrow on top bold. bold B with bold rightwards arrow on top bold right parenthesis the value of θ is:
  • 60o

  • 45o

  • 30o

  • 90o

Solution

A.

60o

bold A with bold rightwards arrow on top bold space bold x bold space bold B with bold rightwards arrow on top bold space equals space AB space sin space space and space stack bold A bold. with bold rightwards arrow on top bold B with bold rightwards arrow on top bold space equals space AB space cos space straight theta.
Given comma space vertical line bold A with bold rightwards arrow on top bold space bold x bold space bold B with bold rightwards arrow on top vertical line space equals space square root of 3 open parentheses stack bold A bold. with bold rightwards arrow on top bold B with bold rightwards arrow on top bold space close parentheses
rightwards double arrow space AB space sin space space straight theta space equals square root of 3 space AB space cos space space straight theta
tan space equals space square root of 3
space straight theta space equals space 60 to the power of 0