The vector `cosalpha\ cosbeta hat i+cosalpha\ sinbeta hat j+sinalpha hat k` is a

Options

A. a) null vector
B. b) unit vector
C. c) constant vector
D. d) none of these

Answer

b) unit vector

Explanation

Given,


`vec r=cosalpha\ cosbeta hat i+cosalpha\ sinbeta hat j+sinalpha hat k`


`|vec r|=sqrt(cos^2alpha cos^2beta+cos^2alpha sin^2beta+sin^2alpha)`


`|vec r|=sqrt(cos^2alpha (cos^2beta+ sin^2beta)+sin^2alpha)`


`|vec r|=sqrt(cos^2alpha (1)+sin^2alpha)`


`|vec r|=sqrt(1)=1`


Hence, correct option is (b)