Obtain the scalar product of unit vectors in Cartesian co - ordinate system .

Explanation

Since `hat(i) , hat(j) and hat(k)` are the unit vectors in the direction of X,Y Z in Cartesian co - ordinate system .
(i) `hat(i) . hat(j) = (1) (1) cos 0^(@) " " [ :. |hat(i)| = 1 , and hat(i) ||hat(i)] `
` :. hat(i) .hat(i) = 1 " " [ :. cos 0^(@) =1] `
similarly `hat(i).hat(j) = 1 and hat(k) .hat(k) = 1 `
(ii) `hat(i) . hat(j) = (1) (1) cos 90^(@)`
`[ :. |hat(i)| = 1 , |hat(j)| = 1 and hat(i) bot hat(j)] `
` :. hat(i) . hat(j) = hat(j) .hat(i) = 0 " " [ :. cos 90^(@) = 0 ] `
similarly `hat(j).hat(k) = hat(k) .hat(j) = 0 `
`hat(k) .hat(i) = hat(i) .hat(k) = 0 `