`(a/bxxc/d) = (axxc)/(bxxd)`

(axxb)xxc=axx(bxxc)

(axxb)xxc=axx(bxxc)

Axx(B-C)=(AxxB)-(BxxC)

Let a, b and c are three vectors hacing magnitude 1, 2 and 3 respectively satisfying the relation [a b c]=6. If hat(d) is a unit vector coplanar with b and c such that b*hat(d)=1 , then evaluate |(axxc)*d|^(2)+|(axxc)xxhat(d)|^(2) .

Prove that axx(bxxc)+bxx(cxxa)+cxx(axxb)=0

If a=2i+5j-7k ,\ b=-3i+4j+k\ a n d\ c=i-2j-3k ,\ compute ( vec axx vec b)xx vec c and axx(bxxc) and verify that these are not equal.

(A-B)xxC -(AxxC)-(AxxC)

Let A={1,2},\ B={1,2,3,4},\ C={5,6}a n d\ D={5,6,7,8} . Verity that: Axx(BnnC)=(AxxB)nn(AxxC)

If A={1,2,3},B={4},C={5}, then verify that: Axx(BuuC)=(AxxB)uu(AxxC)

Theorem 1(i) (For any three set A;B;C ; prove that Axx(BuuC)=(AxxB)uu(AxxC))