If `bar(a),bar(b),bar(c )` are mutually perpendicular unit vectors, then find `[bar(a)bar(b)bar(c )]^(2)`.

If bar(a),bar(b) and bar(c) are mutually perpendicular vectors then [bar(a)bar(b)bar(c)]=

If a,b and c are mutually perpendicular vectors,thenprove that [bar(a)bar(b)bar(c)]^(2)=a^(2)b^(2)c^(2)

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),bar(b) are vectors perpendicular to each other and |bar(a)|=2,|bar(b)|=3, bar(c)timesbar(a)=b, then the least value of 2|bar(c)-bar(a)|" is

If bar(a),bar(b),bar(c) are non-zero,non-coplanar vectors then {bar(a)times(bar(b)+bar(c))}times{bar(b)times(bar(c)-bar(a))} is collinear with the vector

If bar(a),bar(b),bar(c) are non - coplanar vectors, then show the vectors -bar(a)+3bar(b)-5bar(c),-bar(a)+bar(b)+bar(c) and 2bar(a)-3bar(b)+bar(c) are coplanar.

If bar(a),bar(b),bar (c ) are pair wise mutually perpendicular vectors of equal magnitude , then the angle wisv bar(a)+bar(b)+bar (c ) is

Let bar(a),bar(b) be two non zero vectors such that vectors 3bar(a)-5bar(b) and 2bar(a)+bar(b) are mutually perpendicular. If bar(a)+4bar(b) and bar(b)-bar(a) are also mutually perpendicular then the cosine angle between bar(a) and bar(b) is

i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vectors. If bar(a)+bar(b) is collinear with bar(c) and bar(b)+bar(c) is collinear with bar(a) then find the vector bar(a)+bar(b)+bar(c) . ii) If bar(a)+bar(b)+bar(c)=alphabar(d), bar(b)+bar(c)+bar(d)=betabar(a) and bar(a), bar(b), bar(c) are non coplanar vectors, then show that bar(a)+bar(b)+bar(c)+bar(d)=bar(0) .

If bar(a),bar(b)andbar(c) are any three vectors, prove that (1) [bar(a)+bar(b) bar(b)+bar(c) bar(c)+bar(a)]=2[bar(a)bar(b)bar(c)] (2) [bar(a) bar(b)+bar(c) bar(a)+bar(b)+bar(c)]=0