If `veca,vecb,vecc,vecd` respectively, are position vectors representing the vertices A,B,C,D of a parallelogram, then write `vecd` in terms of `veca,vecb` and `vecc`.

If vecc is normal to veca and vecb , show that vecc is normal to veca+vecb and veca-vecb .

Show that the four points A,B,C,D with position vectors veca,vecb,vecc,vecd respectively, such that 3veca-2vecb+5vecc-6vecd=vec0 , are collinear. Also find the position vector of the point of intersection of the lines Ac and BD.

If veca,vecb,vecc are three non-zero vectors such that each one of these is perpendicular to the sum of the other two vectors, then the value of |veca+vecb+vecc|^2 is :

If veca=2hati-3hatj+hatk, vecb=hati+hatk, vecc=2hatj-hatk are three vectors find the area fo the parallelogram having diagonals (veca+vecb) and (vecb+vecc)

If veca, vecb, vecc are unit vectors such that veca+vecb+vecc=0 , find the value of veca cdot vecb + vecb cdot vecc + vecc cdot veca

If veca, vecb, vecc are mutually perpendicular vectors of equal magnitudes, show that the vector veca+vecb+vecc is equally inclined to veca, vecb and vecc .

If veca, vecb and vecc are non-coplanar vectors and lamda is a real number, then the vectors veca + 2vecb + 3vecc, lamda vecb + mu vecc and (2lamda -1)vecc are coplanar when

Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxxvecc)=(sqrt3)/2 (vecb+vecc) . If vecb is not parallel to vecc , then angle between veca and vecb is :

If the volume of the parallelopiped formed by the vectors veca, vecb, vecc as three coterminous edges is 27 units, then the volume of the parallelopiped having vec(alpha)=veca+2vecb-vecc, vec(beta)=veca-vecb and vec(gamma)=veca-vecb-vecc as three coterminous edges, is