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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(2,3,5) AND C(1,5,5)
Asked by haroonrashidgkp | 02 Nov, 2018, 06:46: PM
Expert Answer
begin mathsize 18px style 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 plus 3 straight k
BC space equals straight c minus straight b equals negative 1 straight i plus 2 straight j plus 0 straight k
AB cross times BC equals open vertical bar table row straight i straight j straight k row 1 2 3 row cell negative 1 end cell 2 0 end table close vertical bar
equals negative 6 straight i minus 3 straight j plus 4 straight k
open vertical bar AB cross times BC close vertical bar equals square root of open parentheses negative 6 close parentheses squared plus open parentheses negative 3 close parentheses squared plus open parentheses 4 close parentheses squared end root
equals square root of 61
Area equals fraction numerator square root of 61 over denominator 2 end fraction end style
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