VECTOR A IS PERPINDICULAR TO B HENCE DOT PRODUCT(I.E COS 0=0)
THE SAME WAY VECOT A IS PERPINDICULAR TO C HENCE VECOTR A IS PERPENDICULAR TO BOTH B AND C
consider vector a in x direction
and vector b in y axis and consider vector c in z axis .
vector a and vector b , their dot product is zero as angle bw them is 90 cos90 = 0
similarly a.c = 0
as the condition is satisfied option 3 stands true .
A is perpendicular to B and A is perpendicular to C( by dot product rule) .so A is perpendicular to B and C ie A is perpendicular to the place containing B and C hence A is parallel to BXC
given that A.B=0;
So by this we can conclude that A is perpendicular to B and
given A.C=0;
from this A is perpendicular to C
so definetly B and C lies in same plane and A is perpendicular to this plane
also we know that B cross C is perpendicular to plane containing B and C
hence "A is parallel to B cross to C"