let a,b,c be a system of non coplanar vectors.then the system a1,b1,c1 which satisfies a.a1=b.b1=c.c1=1 and a.b1=a.c1=b.a1=b.c1=c.a1=c.b1=0 is called reciprocal system to the vectors a,b,c then

1) a)[a b c][a1 b1 c1]=product of magnitudes of a cross a1,b cross b1 and c cross c1

b)[a b c][a1 b1 c1]=1

c)a cross a1=b cross b1=c cross c1

d)[a b c][a1 b1 c1]<1

2)a cross a1+b cross b1+c cross c1 is

a)null vector

b)a non zero vector

c){(1/[a b c])power 3}*((a cross a1)cross b)

d)is a scalar multiple of a1+b1+c1

3)which of the following is true

a)a+b+c=(1/[a1 b1 c1])*[b1 cross c1+c1 cross a1]

b)a=(b1 crosss c1)/[a1 b1 c1]

c)b=(a1 cross c1)/[a1 b1 c1]

d)a+b+c=(1/[a b c])*([a1 cross b1+b1 cross c1])

requesting to reply as soon as possible.

sneha goud , 15 Years ago

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