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

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 .

If bar(p)bar(q)bar(r) is reciprocal system of vector triad bar(a),bar(b) and bar(c) then [bar(a)bar(b)bar(c)][bar(p)bar(q)bar(r)]=

If bar(a),bar(b),bar(c) are non-coplanar vectors such that then bar(b)xxbar(c)=bar(a),bar(c)xxbar(a)=bar(b) and bar(a)xxbar(b)=bar(c), then |bar(a)+bar(b)+bar(c)|=

If [bar(a)bar(b)bar(c)]=1 then (bar(a)(bar(b)xxbar(c)))/((bar(c)xxbar(a))*bar(b))+(bar(b)*(bar(c)xxbar(a)))/((bar(a)xxbar(b))*bar(c))+(bar(c)(bar(a)xxbar(b)))/((bar(b)xxbar(c))*bar(a))

If |[bar(a).bar(a), bar(a).bar(b),bar(a).bar(c)], [bar(a).bar(b), bar(b).bar(b), bar(b).bar(c)], [bar(a).bar(c), bar(b).bar(c), bar(c).bar(c)]| =144 then the volume of tetrahedron formed with coterminous edges bar(a) ,bar(b) and bar(c) is equal to

Using properties of scalar triple product, prove that [(bar(a) + bar(b),bar(b) + bar(c), bar(c) + bar(a))] = 2 [(bar(a),bar(b),bar(c))]

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.

For any three non-zero vectors bar(a),bar(b),bar(c),|bar(a)xxbar(b).bar(c)|=|bar(a)||bar(b)||bar(c)| hold if and only if

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

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)]|=