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Question: Answered & Verified by Expert
In a ABC, the sides BC, CA and AB are consecutive positive integers in increasing order. Let a,b and c are position vectors of the vertices A,B and C respectively. If c-a·b-c=0, then the value of a×b+b×c+c×a is equal to
MathematicsVector AlgebraJEE Main
Solution:
2376 Upvotes Verified Answer
The correct answer is: 12
c a b c =0 AC CB =0ΔABC is right angle at C.

From diagram
k2+k+12=k+22
k2+k2+2k+1=k2+4k+4
k2-2k-3=0k=3,-1k-1
So, sides are 3,4,5
Area of ABC=12a×b+b×c+c×a=12×3×4
a×b+b×c+c×a=12

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