13.4.Ex15-28

13.4.Ex15-28 - S E C T I O N 13.4 SOLUTION The Cross...

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SECTION 13.4 The Cross Product (ET Section 12.4) 355 SOLUTION We use the defnition oF the cross product to write v × w = ¯ ¯ ¯ ¯ ¯ ¯ ij k 01 1 1 10 ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ 1 1 ¯ ¯ ¯ ¯ i ¯ ¯ ¯ ¯ 0 1 ¯ ¯ ¯ ¯ j + ¯ ¯ ¯ ¯ 1 1 ¯ ¯ ¯ ¯ k = ( 0 1 ) i ( 0 + 1 ) j + ( 0 1 ) k =− i j k 15. v = D 1 3 , 1 , 1 3 E , w = h− 1 , 1 , 2 i The cross product is the Following vector: v × w = ¯ ¯ ¯ ¯ ¯ ¯ k 1 3 1 1 3 1 12 ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ 1 1 3 ¯ ¯ ¯ ¯ i ¯ ¯ ¯ ¯ 1 3 1 3 ¯ ¯ ¯ ¯ j + ¯ ¯ ¯ ¯ 1 3 1 1 1 ¯ ¯ ¯ ¯ k = µ 2 + 1 3 i µ 2 3 + 1 3 j + µ 1 3 + 1 k = 7 3 i j + 2 3 k 16. v = h 1 , 1 , 0 i , w = h 0 , 1 , 1 i The cross product v × w is the Following vector: v × w = ¯ ¯ ¯ ¯ ¯ ¯ ijk 110 011 ¯ ¯ ¯ ¯ ¯ ¯ = ¯ ¯ ¯ ¯ 11 ¯ ¯ ¯ ¯ i ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ j + ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ k = ( 1 0 ) i ( 1 0 ) j + ( 1 0 ) k = i j + k In Exercises 17–20, calculate the cross product. 17. ( i + j ) × k We use basic properties oF the cross product to obtain ( i + j ) × k = i × k + j × k j + i j i k i × k j j × k = i 18. ( j k ) × ( j + k ) Using properties oF the cross product we get ( j k ) × ( j + k ) = ( j k ) × j + ( j k ) × k = j × j k × j + j × k k × k = 0 + i + i 0 = 2 i 19. ( i + 2 k ) × ( j k )
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This homework help was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.

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13.4.Ex15-28 - S E C T I O N 13.4 SOLUTION The Cross...

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