`overline(ab) + overline(ba)` is completely divisible by 11 and the quotient is `a + b`.

bar(ab)+bar(ba) is completely divisible by 11 and the quotient is a+b.

[[overline(a), overline(b), overline(a)timesoverline(b)]]=

If overline(a), overline(b), overline(c) are non-coplanar vectors and the points with position vectors 2overline(a)+2overline(b), overline(a)+lambdaoverline(b)+overline(c) and 4overline(a)+4overline(b)-5overline(c) are coplanar, then lambda=

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)))=

If overline(a),overline(b),overline( c) are non-zero vectors such that (overline(a)xxoverline(b))xxoverline( c) =(1)/(3)|overline(b)||overline( c) |overline(a), overline( c) ⊥ and theta is the angle between the vectors overline(b) , overline( c) then sin theta= .

If overline(a) and overline(b) are position verctors of A and B respectively, then the position vector of point C in produced AB such that overline(AC)=3overline(AB) is

If overline(c)=2overline(a)+5overline(b), |overline(a)|=a, |overline(b)|=b and the angle between overline(a) and overline(b) is (pi)/(3) , then c^(2) =