The angles with a vector `hat(i)+hat(j)+sqrt(2hat(k))` makes with X,Y and Z axes respectively are

Options

A. `60^(@), 60^(@), 60^(@)`
B. `45^(@), 45^(@), 45^(@)`
C. `60^(@), 60^(@), 45^(@)`
D. `45^(@), 45^(@), 60^(@)`

Answer

C

Explanation

`vec(R)= hat(i) + hat(j) + sqrt2 hat(k)= R_(x) hat(i) + R_(y) hat(j) + R_(y) hat(k) and vec(R)= (R cos alpha) hat(i) + (R cos beta) hat(j) + (R cos gamma) hat(k)`
Now, `R cos alpha= R_(x)=1`
`rArr cos alpha= (1)/(sqrt(1+1+2))= (1)/(2) rArr alpha= 60^(@)`
`R cos beta= 1 rArr beta= 60^(@)`
`R cos gamma= sqrt2 rArr cos gamma= (sqrt2)/(2)= (1)/(sqrt2)`
`rArr gamma= 45^(@)`