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

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

Grade:11

1 Answers

Arun
25758 Points
2 years ago
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)
 
 

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