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 lambda bar c]=[bar a bar b+bar c bar b]` for

If bar(a), bar(b), bar(c) are non coplanar vectors and lambda is a real number, then the vectors bar(a)+2bar(b)+3bar(c), lambdabar(b)+4bar(c) and (2lambda-1)bar(c) are non-coplanar for

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

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

Given four non zero vectors bar a,bar b,bar c and bar d. The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

Given four non zero vectors bar a,bar b,bar c and bar d . The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

Given four non zero vectors bar a,bar b,bar c and bar d . The vectors bar a,bar b and bar c are coplanar but not collinear pair by pairand vector bar d is not coplanar with vectors bar a,bar b and bar c and hat (bar a bar b) = hat (bar b bar c) = pi/3,(bar d bar b)=beta ,If (bar d bar c)=cos^-1(mcos beta+ncos alpha) then m-n is :

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) are two non-collinear vectors such that bar(a)+2bar(b) and bar(b)-lambdabar(a) are collinear, find lambda .

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.

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.