[" For any two vectors "vec a" and "vec b" ,prove that "],[qquad |vec a+vec b|<=|vec a|+|vec b|]

(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]| .

(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]| .

For any two vectors vec a and vec b , prove that: | vec a+ vec b|^2=| vec a|^2+| vec b|^2+2 vec adot vec b , | vec a- vec b|^2=| vec a|^2+| vec b|^2-2 vec adot vec b , | vec a+ vec b|^2+| vec a- vec b|^2=2(| vec a|^2+| vec b|^2) and | vec a+ vec b|^2=| vec a- vec b|^2 iff vec a_|_ vec bdot Interpret the result geometrically.

For any two vectors vec a and vec b , prove that | vec a xx vec b|^(2) = |vec a|^(2)|vec b|^(2) - (vec a . vecb)^(2) = [[veca.veca veca .vecb], [veca.vecb vec b.vecb]]

For any two vectors vec a and vec b prove that | vec a + vec b | <= | vec a | + | vec b |

For any two vectors vec a and vec b , prove that (vec a* vec b)^ 2 le |quad vec a|^2|quad vec b|^2 .

For any two vectors vec a and vec b , prove that (vec a xx vec b )^2= |vec a |^2 |vec b|^2 -(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 aa n d vec b , prove that | vec a+ vec b|lt=| vec a|+| vec b| (ii) | vec a- vec b|lt=| vec a|+| vec b| (iii) | vec a- vec b|geq| vec a|-| vec b|

For any two vectors vec aa n d vec b , prove that | vec a+ vec b|lt=| vec a|+| vec b| (ii) | vec a- vec b|lt=| vec a|+| vec b| (iii) | vec a- vec b|geq| vec a|-| vec b|