Given two vectors and (a) find the magnitude of each vector; (b) use unit vectors to write an expression for the vector difference and (c) find the magnitude of the vector difference Is this the same as the magnitude of Explain.

Solution 53E (a) Given, 2 2 2 Magnitude of vectorA = ( 2.00) + (3.00) + (4.00) Magnitude of vector A = 4 + 9 + 16 Magnitude of vector A = 29 units Similarly, the magnitude of vector (3.00) + (1.00) + ( 3.00) Magnitude of vector B = 9 + 1 + 9 units Magnitude of vector B = 19 units (b) A B = ( 2.00 i + 3.00 j + 4.00 k ) (3.00 i + 1.00 j 3.00 k ) A B = ( 2.00 i 3.00 i ) + (3.00 j 1.00 j ) + (4.00 k ( 3.00 k ) A B = 5.00 i + 2.00 j + 7.00 k (c) The magnitude of the above expression is 2 2 2 | B|= ( 5.00) + (2.00) + (7.00) | | | B|= 25 + 4 + 49 |A B = 78 units | | Now, let us calculate B A. B A = (3.00 i + 1.00 j 3.00 k ) ( 2.00 i + 3.00 j + 4.00 k) B A = 5.00 i 2.00 j 7.00 k The magnitude of the above expression 2 2 2 |B A | (5.00) + ( 2.00) + ( 7.00) |B A = 25 + 4 + 49 | | | | |B A | 78 units Therefore, A B = B A = 78 units | | | | Therefore, both the differences have the same magnitude.