`bar(a),bar(b),bar(c )` are three coplanar vectors, If `bar(a)` is not parallel to `bar(b)`, Show that

bar(a),bar(b),bar(c) are three non-coplanar vectors. If bar(p)=(bar(b)xxbar(c))/(bar(a)*(bar(b)xxbar(c))),bar(q)=(bar(c)xxbar(a))/(bar(a)*(bar(b)xxbar(c))),bar(r)=(bar(a)xxbar(b))/(bar(a)*(bar(b)xxbar(c))) , show that bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=3 .

If bar(a),bar(b),bar(c) are three non zero vectors,then bar(a).bar(b)=bar(a).bar(c)rArr

Let bar(a),bar(b),bar(c) be three non-coplanar vectors and bar(d) be a non-zero vector,which is perpendicularto bar(a)+bar(b)+bar(c). Now,if bar(d)=(sin x)(bar(a)xxbar(b))+(cos y)(bar(b)xxbar(c))+2(bar(c)xxbar(a)) then minimum value of x^(2)+y^(2) is equal to

If bar(a),bar(b),bar(c) are non coplanar vectors and lambda is a real number then [lambda(bar(a)+bar(b))lambda^(2)bar(b)lambdabar(c)]=[bar(a)bar(b)+bar(c)bar(b)] for

If bar(a),bar(b),bar(b),bar(c) are three non coplanar vectors bar(p)=(bar(b)xxbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) then (2bar(a)+3bar(b)+4bar(c))*bar(p)+(2bar(b)+3bar(c)+4bar(a))bar(q)+(2bar(c)+3bar(a)+4bar(b))*bar(r)=

If bar(a),bar(b),bar(c) are three non coplanar vectors bar(p)=((bar(b)xxbar(c)))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) then (2bar(a)+3bar(b)+4bar(c))*bar(p)+(2bar(b)+3bar(c)+4bar(a))*bar(q)+(2bar(c)+3bar(a)+4bar(b))*bar(r)

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

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 non-coplanar unit vectors each including the angle of measure 30^(@) with the other, then find the volume of tetrahedron whose co-terminal edges are bar(a),bar(b),bar(c) .

bar(a)xx(bar(b)xxbar(c)) is parallel to bar(b), then