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x-direction :i
y-direction : j
A(0,2),B=(2√3,0),C(m,1)
AB =OB-OA =2√3i -2j
AC = OC-OB = mi- j
ABxAC
=(2√3i -2j)x(mi- j)
=-2√3k + 2mk
=(-2√3+2m)k
|ABxAC| =|-2√3+2m|
S△ABC=4√3
(1/2)|ABxAC| =4√3
(1/2)|-2√3+2m| =4√3
-2√3+2m = 8√3 or -2√3+2m = -8√3
m=5√3 or -3√3
y-direction : j
A(0,2),B=(2√3,0),C(m,1)
AB =OB-OA =2√3i -2j
AC = OC-OB = mi- j
ABxAC
=(2√3i -2j)x(mi- j)
=-2√3k + 2mk
=(-2√3+2m)k
|ABxAC| =|-2√3+2m|
S△ABC=4√3
(1/2)|ABxAC| =4√3
(1/2)|-2√3+2m| =4√3
-2√3+2m = 8√3 or -2√3+2m = -8√3
m=5√3 or -3√3
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