Prove that
`|vecA.vecB|^2 + |vecA xx vecB|^2 = A^2B^2`

Prove that |veca|-|vecb| le|veca - vecb | .

Prove that |vecaxxvecb|^2=|veca|^2|vecb|^2-(veca*vecb)^2=|:[veca*veca veca*vecb],[veca*vecb vecb*vecb]:| .

Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2 , if and only if veca, vecb are perpendicular, given veca ne vec0, vecb ne vec0 .

Prove that vecaxxvecb ne vecb xx veca if : veca=2hati-3hatj-hatk and vecb=hati+4hatj-2hatk .

If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+ |vecb-vecc|^2 + |vecc^2-veca^2|^2 does not exceed

Let veca = 2hati + hatj-2hatk, and vecb = hati+ hatj if c is a vector such that veca .vecc = |vecc|, |vecc -veca| = 2sqrt2 and the angle between veca xx vecb and vec is 30^(@) , then |(veca xx vecb)|xx vecc| is equal to

Prove that : (vecaxxvecb)^2=|\veca|^2.|\vecb|^2-(veca.vecb)^2 .

For any two vectors veca and vecb , prove that : |veca+vecb|le|veca|+|vecb| . Also, write the name of this inequality