Question

The correct statement among the following, if A and B represent two vectors
a) |A+B|<|A|+|B|
b) |A+B|>|A|+|B|

Answer 1

Isn’t absolute value also known as modulus? :)

Simply square both sides to have

(a+b)2=(a−b)2

⟹a+b)2−(a−b)2=0

⟹4ab=0

⟹ab=0

What do you know when we say a

and b are two vectors and a⋅b=0

?

Projection Theorem:

cosθ=a⋅b|a||b|

If a⋅b=0

, then cosθ=0⟹θ=π2

The vectors a

and b are perpendicular to each other.