Establish the following vector in equalities:
(i) `|vec(a)-vec(b)| le |vec(a)| +|vec(b)|`
(ii) `|vec(a) -vec(b)| ge |vec(a)| - |vec(b)|`
What does the equality sign apply ?

Consider the following inequalities in respect of vector vec(a) and vec(b) 1. |vec(a) + vec(b)| le |vec(a)| + |vec(b)| 2. |vec(a) - vec(b)| ge |vec(a)|- |vec(b)| Which of the above is/are correct?

What is (vec(a)- vec(b)) xx (vec(a) + vec(b)) equal to ?

vec(a) and vec(b) are any two vectors. Prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)|

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-

For any two vectors vec(a) and vec(b) , show that | vec (a).vec(b)| le |vec(a)||vec(b)|

For any two vectors vec(a) and vec(b) , prove that |vec(a)+vec(b)|le|vec(a)|+|vec(b)| .

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

Establish the following vector inequalities geometrically or otherwise: |vec a+ vec b|ge |vec a| -|vec b| . When does the equality sign above apply?

vec(a)+vec(b)+vec(c)=vec(0) such that |vec(a)|=3, |vec(b)|=5 and |vec(c)|=7 . What is |vec(a)+vec(b)| equal to ?