[" 85.Let a,"b" and "c" be three non-zero vectors such that "],[qquad (a times b)times c=(1)/(3)|b|" clla."]

If a, b and c are non-zero vectors such that a times b=c, b times c=a " and "c times a=b then

Let bar(a),bar(b) and bar(c) be non-zero and non collinear vectors such that (bar(a)times bar(b))times bar(c)=(1)/(3)|bar(b)||bar(c)|bar(a) .If theta is the acute angle between the vectors bar(b) and bar(c) then sin theta

Let a,b,c be three non-zero vectors such that a+b+c=0 , then λb×a+b×c+c×a=0, where λ is

Let a.b and c be non-zero vectors such that (a xx b) xx c = (1)/(3) |b| |c| a . If theta is the acute angle between the vectors b and c then sin theta =

Let vec(a), vec(b) and vec(c) be three non-zero vectors such that no two of them are collinear and (vec(a) xx vec(b)) xx vec(c) = (1)/(3) |vec(b)||vec(c)| vec(a) . If theta is the angle between vector vec(b) and vec(c) , then a value of sin theta is

Let overset(to)(a) , overset(to)(b) " and " overset(to)( c) be three non-zero vectors such that no two of them are collinear and (overset(to)(a) xx overset(to)(b)) xx overset(to)( c) = (1)/(3) |overset(to)(b)||overset(to)(c )|overset(to)(a). If 0 is the angle between vectors overset(to)(b) " and " overset(to)(c ) then a value of sin 0 is

Let overset(to)(a) , overset(to)(b) " and " overset(to)( c) be three non-zero vectors such that no two of them are collinear and (overset(to)(a) xx overset(to)(b)) xx overset(to)( c) = (1)/(3) |overset(to)(b)||overset(to)(c )|overset(to)(a). If 0 is the angle between vectors overset(to)(b) " and " overset(to)(c ) then a value of sin 0 is

Suppose a, b, c are three non-zero vectors such that b and c are non-collinear. If (c*c)a=c" and "a times (b times c)+(a*b)b=(4-2beta-sin^(2)alpha)b+(beta^(2)-1)c," then "beta= _______