Three vectors a,b and c satisfy the relation a.b=0 and a.c=0. The vector a is parallel to
A) b
B)c
C) b.c
D) b X c
although i somehow figured D is the answer but i do not know if my procedure was right, ..so.. please..
Answers
answer : option (d) b × c
explanation : 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) ]
Answer:
B cross C
Explanation:
A is only vector perpendicular to vector B and vector C.Hence Vector A parrallel to B cross C.