Question

The vector `(cosalphacosbeta) hat i+(cosalphas inbeta) hat j+(s inalpha) hat k` is a a. null vector b. unit vector c. constant vector d. none of these
A. null vector
B. unit vector
C. a constant vector
D. none of these

Answer 1

Correct Answer - B
Let`vec(a)=(cos alpha cos beta)hat(i)+(cos alpha sin beta) hat(j)+(sin alpha)hat(k)`. Then,
`|vec(a)|^(2)=(cos alphacos beta)^(2)+(cos alpha sin beta)^(2)+(sin alpha)^(2)`
`=cos^(2)alpha cos^(2)beta+cos^(2)alphasin^(2)beta+sin^(2)alpha`
`=cos^(2)alpha(cos^(2)beta+sin^(2)beta)+sin^(2)alpha`
`=(cos^(2)alpha+sin^(2)alpha)=1`.
Hence, the given vector `vec(a)` is a unit vector.