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 xx bar b) + (cos y)(bar b xx bar c) + 2(bar c xx bar a)` then minimum value of `x^2+y^2` is equal to

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+2 bar b+3bar c=bar 0 then bar axxbar b+bar b xx bar c+bar cxx bara = lambda (bar b xx bar c) ,where lambda=

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

bar a and bar b are non- collinear vectors. If barc = (x-2)bar a+bar b and bar d = (2x+1)bar a- bar b are collinear , then find the value of x

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 :

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 = 2bar i + bar k,bar b=bar i+bar j+bar k and bar c=4 bar i-3bar j+7 bar k three vectors. The vector which satisfies bar r xx bar b=bar c xx bar b and bar r.bar a=0 is

IF bar a , bar b , bar c are mutually perpendicular vectors having magnitudes 1,2,3 respectively then [ bar a + bar b + bar c " " bar b - bar a " " bar c ]=?

Let bar(a),bar(b) and bar(c) be three non-zero vectors,no two of which are collinear.If the vectors bar(a)+2bar(b) is collinear with bar(c) and bar(b)+3bar(c) is collinear with bar(a), then bar(a)+2bar(b)+6bar(c) is equal to