Prove that the four points with position vectors `2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc` and `veca-6vecb+6vecc` are coplanar.

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

Show that veca, vecb and vec c are coplanar if veca+vecb,vecb+vecc and vecc+veca are coplanar.

For the non-zero vectors veca, vecb and vecc, veca.(vecbxxvecc) = 0 if

|veca| = |vecb| = veca = vecb .

(-veca).vecbxx(-vecc)) =

If veca=vecb+vecc, then write the value of veca*(vecbxxvecc).

Prove that : |veca + vecb|le|veca|+|vecb| .

Show that the vector area of the triangle whosse vertices have position vector veca,vecb,vecc is 1/2(vecaxxvecb+vecbxxvecc+veccxxveca) .

If veca,vecb and vecc are three vectors such that veca x vecb = vecc and vecb x vecc = veca , then prove that veca,vecb and vecc are mutually at right angles and |vecb| = 1,|vecc| = |veca|