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sol of a, b, c, d are four distinct vectors satisfying the conditions a*b = c *d and a*c = b*d, then prove that a.b+c.d not equal to a.c+b.d.

sol of a, b, c, d are four distinct vectors satisfying the conditions a*b = c *d and a*c = b*d, then prove that a.b+c.d not equal to a.c+b.d.

Grade:11

1 Answers

Vikas TU
14149 Points
one year ago
Dear student 
a,b ,c ,d are four different vectors , 
It is not necessary that they will satify multiplication , 
(a-d) x (b-c)=a x b - a x c - d x b + d x c
=a x b--b x d-d x b-a x b  (a x c = b x d) and (c x d = a x a x b)
=-b x d - d x b
=d x b - d x b  (-b x d = d x b)
=0
since cross product of above  two is zero hence they are parallal

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