Can the magnitude of a vector ever (a) be equal to one of its components, or (b) be less than one of its components? 9. Can a particle with constant speed be accelerating? What if it has constant velocity? ​

a) the other components are zero, in the direction of one of the coordinate axes

b) the magnitude is less than the value of one of its components, it must occur when the vector is in some arbitrary direction

9) constant velocity the acceleration must necessarily be zero,

constant speed  can be accelerated since it may be changing the direction of the velocity vector

Explanation:

Vectors are quantities that have modulo (scalar) direction and sense.

a)  If in a vector its magnitude is equal to one d its components implies that the other components are zero, therefore the vector must be in the direction of one of the coordinate axes

b) if the magnitude is less than the value of one of its components, it must occur when the vector is in some arbitrary direction, other than the direction of the axes, that is

          R² = x² + y²

where R is the magnitude of the vector e x, and are the components

9) When a particle has a constant velocity, the acceleration must necessarily be zero,

         v = vo + a t

The bold letters indicate vectors If a = 0 implies that v = vo

If a particle has constant speed it can be accelerated since it may be changing the direction of the velocity vector, this type of acceleration has the name of centripetal acceleration

a straight line sloped