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 vector vec a\ a n d\ vec b prove that | vec a+ vec b|lt=| vec a|+| vec b|dot

For any two vectors vec a\ a n d\ vec b write when | vec a+ vec b|=| vec a|+| vec b| holds.

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 , show that : ( vec a+ vec b)dot( vec a- vec b)=0, when | vec a|=| vec b|dot

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 aa n d vec b , show that (1+| vec a|^2)(1+| vec b|^2)={"("1+ vec a.vec b")"^2| vec a+ vec b+( vec axx vec b)|^2

Find the angle between two vectors vec a and vec b , if | vec a xx vec b|= vec a . vec b .

For any three vectors vec a , vec b , vec c , prove that | vec a+ vec b+ vec c|^2=| vec a|^2+| vec b|^2+| vec c|^2+2( vec adot vec b+ vec bdot vec c+ vec cdot vec a)

If two vectors vec a and vec b are such that | vec a|=2,| vec b|=1 and vec adot vec b=1 , find (3 vec a-5 vec b)dot(2 vec a+7 vec b)dot

For any tow vectors a\ a n d\ b show that ( vec a+ vec b) ( vec a- vec b)=0 if | vec a|=| vec b|dot