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Unformatted text preview: Tutorial VAM: Vector Algebra and an Introduction to Matrices 9. Solutions to Exercises and Problems Exercise 1. j A Â¢ B j = AB j cos Î¼ j Â· AB since j cos Î¼ j Â· 1 : Exercise 2. j A + B j = p ( A + B ) Â¢ ( A + B ) = p A 2 + B 2 + 2 A Â¢ B Â· p A 2 + B 2 + 2 AB = q ( A + B ) 2 = A + B: Exercise 3. Consider the sides of the triangle as vectors, oriented such that C = A Â¡ B : Then, C 2 = ( A Â¡ B ) Â¢ ( A Â¡ B ) = A 2 + B 2 Â¡ 2 A Â¢ B = A 2 + B 2 Â¡ 2 AB cos Î¼ C : Exercise 4. The magnitude of both sides is clearly the same. However, using the righthand rule on the left hand side (rotating B into A ) results in a direction that is exactly opposite to that obtained from the rotation of A into B : The negative sign denotes this reverse of direction. Exercise 5. Scalar products: ^ x Â¢ ^x = ^y Â¢ ^y = ^ z Â¢ ^ z = 1; ^x Â¢ ^y = ^ x Â¢ ^z = ^y Â¢ ^ z = 0 Vector products: ^x Â£ ^x = ; ^x Â£ ^ y = ^z ^ x Â£ ^ z = Â¡ ^ y ^ y Â£ ^x = Â¡ ^z ^y Â£ ^ y = ; ^y Â£ ^z = ^ x ^z Â£ ^x = ^y ^ z Â£...
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This note was uploaded on 07/13/2008 for the course PHY 201 taught by Professor Covatto during the Spring '08 term at ASU.
 Spring '08
 COVATTO

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