If (a+b),(b+c)and (c+a) are coplanar then a×(b×c) is?
0
1
a.b
b.c
Find the value of a×(b×c):
Given that (a+b),(b+c)and (c+a) are coplanar.
Therefore,
⇒(a+b)[(b+c)x(c+a)]=0⇒(a+b)(bxc+bxa+cxc+cxa)=0⇒(a+b)(bxc+bxa+cxa)=0⇒a.(bxc)+a.(bxa)+a.(cxa)+b.(bxc)+b.(bxa)+b.(cxa)=0⇒[abc]+0+0+0+0=0⇒[abc]=0⇒a×(b×c)=0
Hence, the correct option is (A).