Three vectors `overline A, overline B and overline C` add up to zero. Find which is false.

For three vectors overline(p),overline(q) and overline ( r) , if overline( r) =3 overline(p)+4overline(q) and 2 overline( r) = overline(p) - 3overline(q) then

For vectors overline(a) and overline(b) and overline(a)+overline(b)ne=0 and overline(c) is a non-zero vector, then (overline(a)+overline(b))times(overline(c)-(overline(a)+overline(b)))=

overline(a), overline(b) are vectors, overline(AB), overline(BC) determined by two adjacent sides of a regular hexagon ABCDEF.The vector represented by overline(EF) is

If overline(a),overline(b), overline(c) are three non-coplanar vectors and overline(p), overline(q), overline(r) are vectors defined by the relations overline(p)=(overline(b)timesoverline(c))/([[overline(a), overline(b), overline(c)]]), overline(q)=(overline(c)timesoverline(a))/([[overline(a), overline(b), overline(c)]]), overline(r)=(overline(a)timesoverline(b))/([[overline(a), overline(b), overline(c)]]) , then (overline(a)+overline(b))*overline(p)+(overline(b)+overline(c))*overline(q)+(overline(c)+overline(a))*overline(r)=

The vectors overline(a) lies in the plane of vectors overline(b) and overline(c) . Which of the following is correct?

[[overline(a), overline(b), overline(c)]] is the scalar triple product of three vectors overline(a), overline(b), overline(c) then [[overline(a), overline(b), overline(c)]]=

If overline(x)*overline(a)=0, overline(x)*overline(b)=0, overline(x)*overline(c)=0 for some non-zero vectors overline(x) , then [[overline(a), overline(b), overline(c)]]=0 is

ABCDE is a pentagon. The resultant of the vectors overline(AB), overline(AE), overline(BC), overline(DC), overline(ED) and overline(AC) in terms of overline(AC) is

If overline(a), overline(b) and overline(c) are unit vectors perpendicular to each other, the [[overline(a), overline(b), overline(c)]]^(2)=