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

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

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)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

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

If bara,barb,barc are non-coplanar vectors then [bar(a)+2bar(b)" "bar(a)+bar(c)" "bar(b)]=

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

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 .

bar(a)+2bar(b)+3bar(c)=bar(0) and bar(a)xxbar(b)+bar(b)xxbar(c)+bar(c)xxbar(a)=iota(bar(b)xxbar(c)), then iota=