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Vector Algebra

Question
CBSEENMA12036194
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ABC is a triangle, right angled at A. The resultant of the forces acting along AB with rightwards arrow on top space comma space AC with rightwards arrow on top space space with space magnitudes space 1 over AB space and space 1 over AC respectively is the force along AD with rightwards arrow on top where D is the foot of the perpendicular from A onto BC. The magnitude of the resultant is

  • fraction numerator AB squared space plus space AC squared over denominator left parenthesis AB right parenthesis squared plus left parenthesis AC right parenthesis squared end fraction
  • fraction numerator left parenthesis AB right parenthesis left parenthesis AC right parenthesis over denominator AB space plus space AC end fraction
  • 1 over AB plus 1 over AC
  • 1 over AD

Solution

D.

1 over AD Magnitude space of space resultant space equals space square root of open parentheses 1 over AB close parentheses squared space plus open parentheses 1 over AC close parentheses squared end root space equals space fraction numerator square root of AB squared plus AC squared end root over denominator AB. AC end fraction space equals space fraction numerator BC over denominator AB. AC end fraction space equals space fraction numerator BC over denominator AD. BC end fraction space equals space 1 over AD

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