A vector V makes an angle `theta` with the hori-zontal. The vector is rotated through an angle `alpha` . Does this rotaion change the vector V ?

Explanation

Magnitude of vector = V ,
Let initial angle with horizontal = `theta`
Angle rotated `alpha`
So new angle with horizontal = ` theta + alpha`
Now horizontal component,
`V_(alpha) = ` V cos `(theta + alpha)`
Vertical component, `V_(y) = ` V sin `(theta + alpha )`
Magnitude of vector, V = `sqrt(V_(x)^(2) + V_(y)^(2)) = V `
So rotating the vector does not change its magnitude.