If three vectors along coordinate axis represent the adjacent sides of a cube of length b, then the unit vector along its diagonal passing through the origin will be

Options

A. `(hat(i)+hat(j)+hat(k))/(sqrt(2))`
B. `(hat(i)+hat(j)+hat(k))/(sqrt(36))`
C. `hat(i)+hat(j)+hat(k)`
D. `(hat(i)+hat(j)+hat(k))/(sqrt(3))`

Answer

D

Explanation

(d) Diagonal vector, `A=bhat(i)+bhat(j)+bhat(k)`
` "or "A=sqrt(b^(2)+b^(2)+b^(2))=sqrt(3)b`
`:.A=(A)/|A|=(hat(i)+hat(j)+hat(k))/(sqrt(3))`