|bar(a)+bar(b)|<|bar(a)|+|bar(b)|bar(vec a)|^(2 pi)bar(b)

If bar(a),bar(b),bar(c) are coplanar then the value of |[bar(a),bar(b),bar(c)],[bar(a)*bar(a),bar(a)*bar(b),bar(a)*bar(c)],[bar(b).bar(a),bar(b)*bar(b),bar(b)*bar(c)]|=

The non-zero vectors bar(a) , bar(b) , bar(c ) holds | (bar(a) .bar(b) ).bar( c) |=| bar(a) ||bar(b)|| bar( c) if

If (bar(a), bar(b))=60^(@)" then "(-bar(a), -bar(b))=

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), bar(c) form a left handed orthogonal system and bar(a)*bar(a)=4, bar(b)*bar(b)=9, bar(c)*bar(c)=16 then [bar(a) bar(b) bar(c)] =

If (bar(a),bar(b))=(pi)/(6),bar(c) is perpendicular to bar(a) and bar(b),|bar(a)|=3,|bar(b)|=4,|bar(c)|=6 then |[bar(a)bar(b)bar(c)]|

[bar(a)" "bar(b)+bar(c)" "bar(a)+bar(b)+bar(c)]=0

([[bar(a),bar(b),bar(c)]])/([[bar(b),bar(a),bar(c)]]) =

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