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 | 2nd 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

Answered by Arun | 12th Nov, 2018, 10:21: AM