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CBSE Class 12-science Answered

 using vectors find the area of triangle ABC whose vertices are:

  1. A(1,-1,2) B(2,1,-1)AND C(3,-1,2)
Asked by haroonrashidgkp | 02 Nov, 2018, 06:47: PM
Expert Answer
begin mathsize 18px style using space vectors space find space the space area space of space
triangle space ABC space whose space vertices space are colon space space
straight A left parenthesis 1 comma negative 1 comma 2 right parenthesis space straight B left parenthesis 2 comma 1 comma negative 1 right parenthesis AND space straight C left parenthesis 3 comma negative 1 comma 2 right parenthesis
Area space of space triangle space is
1 half open vertical bar AB cross times BC close vertical bar
AB equals straight b minus straight a equals 1 straight i plus 2 straight j minus 3 straight k
BC space equals straight c minus straight b equals 1 straight i minus 2 straight j plus 3 straight k
AB cross times BC equals open vertical bar table row straight i straight j straight k row 1 2 cell negative 3 end cell row 1 cell negative 2 end cell 3 end table close vertical bar
equals 0 straight i minus 6 straight j minus 4 straight k
open vertical bar AB cross times BC close vertical bar equals square root of open parentheses 0 close parentheses squared plus open parentheses negative 6 close parentheses squared plus open parentheses negative 4 close parentheses squared end root
equals 2 square root of 13
Area equals fraction numerator 2 square root of 13 over denominator 2 end fraction end style
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