NIMCET 2015 Question Paper with solutions

Question : 3 of 120

Marks: +1, -0

a↖{→}, b↖{→}

and

c↖{→}

are the position vectors of the verticesA, B, C of triangle ABC, then the area of the triangleABC is :

Solution:

We have a,b and c are the position vectors of the vertices of A B and C of a ΔABC.
Area of triangle ABC

=1/2|AB×AC|

=1/2|(b-a)×(c-a)|

=1/2|(b×c)+(a×b)+(c×a)+a×a|

=1/2|(a×b)+b×c+c×a|

[∵a×a=0]

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