If `bar(a),bar(b),bar(c)` are non-zero, non -coplanar vectors, then show that the vectors `2bar(a)-5bar(b)+2bar(c),bar(a)+5bar(b)-6bar(c)and3bar(a)-4bar(c)` are coplanar.

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 non -zero,non - coplanar vectors and bar(a)+bar(b)+bar(c) , -a+8bar(b)+7bar(c) , 5bar(a)+lambdabar(b)-3bar(c) are coplanar,then the value of |lambda| is

If bar(a),bar(b),bar(c) are non-coplanar vectors.Prove that the four points -bar(a)+4bar(b)-3bar(c) , 3bar(a)+2bar(b)-5bar(c) , -3bar(a)+8bar(b)-5bar(c) , -3bar(a)+2bar(b)+bar(c) are coplanar.

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)|=

(bar(a)+2bar(b)-bar(c))*(bar(a)-bar(b))xx(bar(a)-bar(bar(c)))=

If [bar(a)+2bar(b)2bar(b)+bar(c)5bar(c)+bar(a)]=k[bar(a)bar(b)bar(c)]

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

let bar(a),bar(b)&bar(c) be three non-zero non coplanar vectors and bar(p),bar(q)&bar(r) be three vectors defined as bar(p)=bar(a)+bar(b)-2bar(c);bar(q)=3bar(a)-2bar(b)+bar(c)&bar(r)=bar(a)-4bar(b)+2bar(c) .If v_(1),v_(2) are the volumes of parallelopiped determined by the vectors bar(a),bar(b),bar(c) and bar(p),bar(q),bar(r) respectively then v_(2):v_(1) is

If [(bar(a)+2bar(b)+3bar(c))times(bar(b)+2bar(c)+3bar(a))].(bar(c)+2bar(a)+3bar(b))=54 , where bar(a),bar(b)&bar(c) are 3 non coplanar vectors then |[bar(a).bar(a)quad bar(a).bar(b)quad bar(a).bar(c)],[bar(b).bar(a)quad bar(b).bar(b)quad bar(b).bar(c)],[bar(c).bar(a)quad bar(c).bar(b)quad bar(c).bar(c)]|

Let bar(a),bar(b),bar(c) are three non-coplanar vectors such that bar(r)_(1)=bar(a)-bar(b)+bar(c);bar(r)_(2)=bar(b)+bar(c)-bar(a);bar(r)_(3)=bar(c)+bar(a)+bar(b),bar(r)=2bar(a)-3bar(b)+4bar(c) .If bar(r)=lambda_(1)bar(r)_(1)+lambda_(2)bar(r)_(2)+lambda_(3)bar(r)_(3) then lambda_(1)+lambda_(2)+lambda_(3) is equal to