For any two vectors ` vec a` and ` hat b` , show that : `( vec a+ vec b)dot( vec a- vec b)=0| vec a|=| vec b|dot`

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 a and vec b, show that |vec a*vec b|<=|vec a||vec b|

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

For any tow vectors a and b show that (vec a+vec b)vec a-vec b=0hArr|vec a|=|vec b|

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 and vec b, we always have |vec a+ vec b|<=|vec a|+|vec b|

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 vector vec a and vec b prove that |vec a+vec b|<=|vec a|+|vec b|

Two vectors vec A and vec B are such that vec A + vec B = vec A- vec B , then

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector,) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0