1)

  For any three vectors a,b and c , [a+b, b+c, c+a] is


A) [a b c]

B) 3 [a b c]

C) 2[a b c ]

D) 0

Answer:

Option C

Explanation:

 [a+b , b+c, c+a]

= (a+b).[(b+c) x (c+a)]

= (a+b).[b x c +b x a+c x c+ c x a]

= (a+b).(b x c +b x a+ c x a)

                            [$\because$ c x c=0]

 = a.(b x c)+ a.(b x a)+a. (c x a)+ b. (bx c)+b. (b x a)+b.(c x a)

 =a.(b x c)+b. (c x a)

 =[a b c]+[a b c]

=2[a b c]