If `bara,barb,barc` are non-coplanar vectors, express `bara times (barb times barc)` as a linear combination of `bara,barb,barc`

Prove that [bara times barb bara times barc bard]=(bara.bar d)[bara barb barc]

If vectors barb, bar c ,bard are not coplanar then prove that (bara times barb) times (barc times overlind)+(bara times barc) times (bard times barb)+(bara times bard) times (barb times barc) is parallel to bara .

If bara ,barb and barc are three unit vectors such that bara times (barb times barc)=1/2 barb Find the angles which bara makes with barb and barc .

IF barx times barb=barc times barb and barx . bara =0 then barx=

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

If barc=bara times barb and barb=barc times bara then

For three non-coplanar vectors bara,barb,barc the relation |(bara times barb).barc|=|bara||barb||barc| holds true , if

bara times (barb times barc) +barb times (barc times bara)+ barc times (bara times barb) equals

VECTOR ALGEBRA | LINEAR COMBINATION LINEAR INDEPENDENCE AND LINEAR DEPENDENCE | Definition and physical interpretation: Linear Combination, Linear Combination: Linear Independence And Linear Dependence, Linearly Independent, Linearly Dependent, Theorem 1: If veca and vecb are two non collinear vectors; then every vector vecr coplanar with veca and vecb can be expressed in one and only one way as a linear combination: x veca +y vecb ., Theorem 2: If veca , vecb and vecc are non coplanar vectors; then any vector vecr can be expressed as linear combination: x veca +y vecb +z vecc , Theorem 3:If vectors veca , vecb and vecc are coplanar then det( veca vecb vecc ) = 0, Examples: Prove that the segment joining the middle points of two non parallel sides of a trapezium is parallel to the parallel sides and half of their sum., Components of a vector in terms of coordinates of its end points

If barr.bara=barr.barb=barr.barc=0 for non-zero vector barr then the value of (bara barb barc) is