For any two vectors `veca and vecb,` prove that `((veca )/(|vec a |^2)-(vecb)/(| vec b|^2))^2=(( vec a -vecb)/(| vec a || vec b |))^2`

For any two vectors veca and vecb prove that |veca+vec|le|veca|+|vecb|

For any two vectors veca and vecb prove that |veca-vec|le|veca|+|vecb|

For any two vectors veca and vecb prove that |veca-vec|ge|veca|-|vecb|

For any two vectors vec a and vec b, prove that ((vec a) / (| vec a | ^ (2)) - (vec b) / (| vec b | ^ (2))) ^ (2) = ((vec a-vec b) / (| vec a || vec b |)) ^ (2)

For any two vectors vec a and vec b ,prove that (vec a xxvec b)^(2)=|vec a|^(2)|vec b|^(2)-(vec a*vec b)^(2)

For any two vectors vec a\ a n d\ vec b prove that | vec axx vec b|^2=| (veca. veca , veca. vecb),(vecb.veca ,vecb.vecb)|

(22) if vec p and vec q are unit vectors forming an angle of 30^@ ; find the area of the parallelogram having veca=vecp+2vecq and vecb=2vecp+vecq as its diagonals. (23) For any two vectors vec a and vec b , prove that | vec a xxvec b|^2=| [vec a* vec a ,vec a*vec b],[ vec b* vec a, vec b* vec b]| .

If two vectors vec aa n d vec b are such that |veca|=3, |vecb|=2 and veca.vecb=6, . , Find | vec a+ vec b|a n d| vec a- vec b|dot

If veca, vecb, vec c are three non coplanar vectors , then the value of (vec a.(vec b xx vec c) )/((vec c xx vec a).vec b) + ( vecb.(vec a xx vec c ))/(vec c.(vec a xx vec b)) is