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) , we always have |vec(a).vec(b)| le |vec(a)||vec(b)| . (Cauchy Schwartz inequality)

For any two vectors vec(a) and vec(b) , we always have |vec(a)+vec(b)|le|vec(a)|+|vec(b)| (triangle inequality).

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 + vec b | <= | vec a | + | vec b |

For any two vectors vec a and 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 write then |vec a+vec b|=|vec a|+|vec b| holds.

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* vec b)^ 2 le |quad vec a|^2|quad vec b|^2 .