compute the modulus of any given vector up to 2 and 3 dimension?

Answer 1

Modulus of a vector is its magnitude.

X=(x1, x2, x3) (this is a 3-D vector)
Using Pythagorean theorem
|X|=sqrt(x1^2 + x2^2 + x3^2)

In general
|X|=SUM(xn^2) from 1 to N where N is the number of dimensions.