Three vectors satisfy the relation A.B=0 , then A is parallel toB*C.b.B.cc. C.d.B

There are three vectors a, b and c satisfying the relation,

 

a.b = 0 and a.c = 0

 

a.b = 0 => dot product of a and b = 0 it means angle between vector a and vector b is 90°.

 

similarly, a.c = 0 => dot product of a and c = 0, it means angle between vector a and c is 90°.

 

option (a) is incorrect, a is not parallel to b rather, a and b is perpendicular to each other.

 

option (b) is incorrect, because a is perpendicular on c.

 

option (c) is incorrect because b.c is an scalar quantity and a scalar can't parallel to a vector quantity.

 

option (d) correct because cross product of b and c is perpendicular on plane of b and c. and we know, from above explanation only a is perpendicular on b and c too. hence, vector b × c is parallel to vector a.

 

[ note : for batter understanding let's assume that a = i, b = j and c = k, here a.b = i.j = 0, a.c = j.k = 0, then, b × c = j × k = i = a hence, a is parallel to (b × c)