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Obtain the scalarproduct of unit vectors in Cartesian co - ordinatesystem . |
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Answer» Solution :Since `HAT(i) , hat(j) and hat(k)` are the unit vectors in the direction of X,Y Z in Cartesian co - ordinatesystem . (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 ` |
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