The vectors `vec(a), vec(b), vec(c) and vec(d)` are such that `vec(a)xx vec(b) = vec(c) xx d and vec(a) xx vec(c)= vec(b) xx vec(d)`. Which of the following is/are correct?
`1. (vec(a)-vec(d))xx (vec(b)-vec(c))=vec(0)`
2. `(vec(a)xx vec(b))xx (vec(c)xx vec(d))=vec(0)`
Select the correct answer using the code given below :

Options

A. 1 only
B. 2only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

C

Explanation

`(vec(a)-vec(d))xx(vec(b)-vec(c))`
`=vec(a)xxvec(b)-vec(d)xxvec(b)-vec(a)xxvec(c)+vec(d)xxvec(c)`
`=vec(c)xxvec(d)-vec(d)xxvec(b)-vec(b)xxvec(d)-vec(c)xxvec(d)`
`=-vec(d)xxvec(b)+vec(d)xxvec(b)`
= 0
again `(vec(a)xxvec(b))=(vec(c)xxvec(d))` given
`rArr (vec(a)xxvec(b))xx(vec(c)xxvec(d))=(vec(c)xxvec(d))xx(vec(c)xxvec(d))=0 ("as" vec(a)xxvec(a)=0)`
So both (1) and (2) are correct.