The angle between `(bar(A)timesbar(B)))` and `(bar(B)timesbar(A))` is (in radian)

If |bar(a)|=4,|bar(b)|=2 and the angle between bar(a) and bar(b) is pi/6 ,then (bar(a)timesbar(b))^(2) is equal to

Let bar(a)=2hat i+hat j-2hat k,bar(b)=hat i+hat j and bar(c) be a vector such that |bar(c)-bar(a)|=3,|(bar(a)timesbar(b))timesbar(c)|=3 and the angle between bar(c) and bar(a)timesbar(b) is 30^(@) . Then, bar(a).bar(c) is equal to

If |bar(a)|=4,|bar(b)|=2 and the angle between bar(a) and bar(b) is pi/6 ,then (|bar(a)timesbar(b)|)^(2) is equal to

Let bar(a),bar(b),bar(c) be vectors of equal magnitude such that the angle between bar(a) and bar(b) is alpha,bar(b) and bar(c) is beta and bar(c) and bar(a) is gamma. Then the minimum value of cos alpha+cos beta+cos gamma is

The point of intersection of the lines bar(r)timesbar(a)=bar(b)timesbar(a) and bar(r)timesbar(b)=bar(a)timesbar(b) is 1. bar(a)-bar(b) 2. bar(a)+bar(b) 3. 2bar(a)+3bar(b) 4. 3bar(a)-2bar(b)

If bar(a),bar(b),bar(c) are non-coplanar unit vectors such that bar(a)times(bar(b)timesbar(c))=(sqrt(3))/(2)(bar(b)+bar(c)) then the angle between bar(a) and bar(b) is ( bar(b) and bar(c) are non collinear)

If bar(a),b,bar(c) are non-coplanar unit vectors such that bar(a)times(bar(b)timesbar(c))=(sqrt(3))/(2)(bar(b)+bar(c)) then the angle between bar(a) and bar(b) is (bar(b) and bar(c) are non collinear)

If theta is the angle between unit vectors bar(A) and bar(B) then (1-bar(A).bar(B))/(1+bar(A)*bar(B)) is equal to

If theta is the angle between unit vectors bar(A) and bar(B) then (1-bar(A).bar(B))/(1+bar(A)*bar(B)) is equal to (A) tan^(2)((theta)/(2)) (B) sin^(2)((theta)/(2)) (C) cot^(2)((theta)/(2)) (D) cos^(2)((theta)/(2))

If [bar(a) bar(b) bar(c)]=2 then [2(bar(b)timesbar(c))(bar(-c)timesbar(a))(bar(b)timesbar(a))] is equal to