undefined Solution The value of a · ( b − c ) , ( a − b ) · c if a = [ 1 , − 3 , 5 ] , b = [ 4 , 0 , 8 ] , c = [ − 2 , 9 , 1 ] . The value of a · ( b − c ) is 68 _ and ( a − b ) · c is − 24 _ . Definition used: Inner Product of vectors: The inner product or dot product a · b of two vectors a and b is the product of their lengths times the cosine of their angle. a · b = | a | | b | cos γ if a ≠ 0 , b ≠ 0 a · b = 0 if a = 0 or b = 0 The angle γ is 0 ≤ γ ≤ π , between a and b is measured when the initial points of the vectors coincide. In component form, a · b = a 1 b 1 + a 2 b 2 + a 3 b 3 where a = [ a 1 , a 2 , a 3 ] , b = [ b 1 , b 2 , b 3 ] Calculation: Substitute b = [ 4 , 0 , 8 ] , c = [ − 2 , 9 , 1 ] in b − c as, b − c = [ 4 , 0 , 8 ] − [ − 2 , 9 , 1 ] = [ 4 + 2 , 0 − 9 , 8 − 1 ] = [ 6 , − 9 , 7 ] Substitute a = [ 1 , − 3 , 5 ] , b = [ 4 , 0 , 8 ] in a − b as, a − b = [ 1 , − 3 , 5 ] − [ 4 , 0 , 8 ] = [ 1 − 4 , − 3 − 0 , 5 − 8 ] = [ − 3 , − 3 , − 3 ] Use above definition and substitute a = [ 1 , − 3 , 5 ] and b − c = [ 6 , − 9 , 7 ] in a · ( b − c ) . a · ( b − c ) = [ 1 , − 3 , 5 ] · [ 6 , − 9 , 7 ] = 1 ( 6 ) + ( − 3 ) ( − 9 ) + ( 5 ) ( 7 ) = 6 + 27 + 35 = 68 Substitute c = [ − 2 , 9 , 1 ] and a − b = [ − 3 , − 3 , − 3 ] in ( a − b ) · c . ( a − b ) · c = [ − 2 , 9 , 1 ] · [ − 3 , − 3 , − 3 ] = − 2 ( − 3 ) + ( 9 ) ( − 3 ) + 1 ( − 3 ) = 6 − 27 − 3 = − 24 Therefore, the value of a · ( b − c ) is 68 _ and ( a − b ) · c is − 24 _ .

10th Edition

ISBN: 9781119664697

Author: Kreyszig

Publisher: WILEY

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Chapter 9.2, Problem 9P

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Chapter 9 Solutions

ADVANCED ENGINEERING MATHEMATICS

Ch. 9.1 - Prob. 1P Ch. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P Ch. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...

Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 13P Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 17P Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - What laws do Probs. 12–16 illustrate? 12. (a + b)...Ch. 9.1 - Prob. 20P Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Prob. 22P Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Equilibrium. Find v such that p, q, u in Prob. 21...Ch. 9.1 - Find p such that u, v, w in Prob. 23 and p are in...Ch. 9.1 - Unit vector. Find the unit vector in the direction...Ch. 9.1 - Restricted resultant. Find all v such that the...Ch. 9.1 - Prob. 30P Ch. 9.1 - For what k is the resultant of [2, 0, −7], [1, 2,...Ch. 9.1 - If |p| = 6 and |q| = 4, what can you say about the...Ch. 9.1 - Same question as in Prob. 32 if |p| = 9, |q| = 6,...Ch. 9.1 - Relative velocity. If airplanes A and B are moving...Ch. 9.1 - Same question as in Prob. 34 for two ships moving...Ch. 9.1 - Prob. 36P Ch. 9.1 - Prob. 37P Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 8P Ch. 9.2 - Prob. 9P Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 11P Ch. 9.2 - What does u • v = u • w imply if u = 0? If u ≠...Ch. 9.2 - Prove the Cauchy–Schwarz inequality. Ch. 9.2 - Verify the Cauchy–Schwarz and triangle...Ch. 9.2 - Prob. 15P Ch. 9.2 - Triangle inequality. Prove Eq. (7). Hint. Use Eq....Ch. 9.2 - Prob. 17P Ch. 9.2 - Prob. 18P Ch. 9.2 - Prob. 19P Ch. 9.2 - Prob. 20P Ch. 9.2 - Prob. 21P Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - What will happen to the angle in Prob. 24 if we...Ch. 9.2 - Prob. 26P Ch. 9.2 - Addition law. cos (α − β) = cos α cos β + sin α...Ch. 9.2 - Prob. 28P Ch. 9.2 - Prob. 29P Ch. 9.2 - Prob. 30P Ch. 9.2 - Prob. 31P Ch. 9.2 - Prob. 32P Ch. 9.2 - Prob. 33P Ch. 9.2 - Prob. 34P Ch. 9.2 - Prob. 35P Ch. 9.2 - Prob. 36P Ch. 9.2 - Prob. 37P Ch. 9.2 - Prob. 38P Ch. 9.2 - Prob. 39P Ch. 9.2 - Prob. 40P Ch. 9.3 - Prob. 1P Ch. 9.3 - Prob. 2P Ch. 9.3 - Prob. 3P Ch. 9.3 - Prob. 4P Ch. 9.3 - Prob. 5P Ch. 9.3 - Prob. 6P Ch. 9.3 - Prob. 7P Ch. 9.3 - Prob. 8P Ch. 9.3 - Prob. 9P Ch. 9.3 - Prob. 11P Ch. 9.3 - Prob. 12P Ch. 9.3 - Prob. 13P Ch. 9.3 - Prob. 14P Ch. 9.3 - Prob. 15P Ch. 9.3 - Prob. 16P Ch. 9.3 - Prob. 17P Ch. 9.3 - Prob. 18P Ch. 9.3 - Prob. 19P Ch. 9.3 - Prob. 20P Ch. 9.3 - Prob. 21P Ch. 9.3 - Prob. 22P Ch. 9.3 - Prob. 23P Ch. 9.3 - Prob. 25P Ch. 9.3 - Prob. 26P Ch. 9.3 - Prob. 27P Ch. 9.3 - Prob. 28P Ch. 9.3 - Prob. 29P Ch. 9.3 - Prob. 30P Ch. 9.3 - Prob. 31P Ch. 9.3 - Prob. 32P Ch. 9.3 - Prob. 33P Ch. 9.3 - Prob. 34P Ch. 9.4 - Prob. 1P Ch. 9.4 - Prob. 2P Ch. 9.4 - Prob. 3P Ch. 9.4 - Prob. 4P Ch. 9.4 - Prob. 5P Ch. 9.4 - Prob. 6P Ch. 9.4 - Prob. 7P Ch. 9.4 - Prob. 9P Ch. 9.4 - Prob. 10P Ch. 9.4 - Prob. 11P Ch. 9.4 - Prob. 12P Ch. 9.4 - Prob. 13P Ch. 9.4 - Prob. 14P Ch. 9.4 - Prob. 15P Ch. 9.4 - Prob. 16P Ch. 9.4 - Prob. 17P Ch. 9.4 - Prob. 18P Ch. 9.4 - Prob. 19P Ch. 9.4 - Prob. 20P Ch. 9.4 - Prob. 22P Ch. 9.4 - Prob. 23P Ch. 9.4 - Prob. 24P Ch. 9.5 - Prob. 1P Ch. 9.5 - Prob. 2P Ch. 9.5 - Prob. 3P Ch. 9.5 - Prob. 4P Ch. 9.5 - Prob. 5P Ch. 9.5 - Prob. 6P Ch. 9.5 - Prob. 7P Ch. 9.5 - Prob. 8P Ch. 9.5 - Prob. 9P Ch. 9.5 - Prob. 10P Ch. 9.5 - Prob. 11P Ch. 9.5 - Prob. 12P Ch. 9.5 - Prob. 13P Ch. 9.5 - Prob. 14P Ch. 9.5 - Prob. 15P Ch. 9.5 - Prob. 16P Ch. 9.5 - Prob. 17P Ch. 9.5 - Prob. 18P Ch. 9.5 - Prob. 19P Ch. 9.5 - Prob. 20P Ch. 9.5 - Prob. 21P Ch. 9.5 - r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)Ch. 9.5 - r(t) = [cos t, sin t, 9t], P: (1, 0, 18)Ch. 9.5 - Prob. 27P Ch. 9.5 - Prob. 29P Ch. 9.5 - Prob. 30P Ch. 9.5 - Prob. 31P Ch. 9.5 - Prob. 32P Ch. 9.5 - Prob. 33P Ch. 9.5 - Prob. 34P Ch. 9.5 - Prob. 35P Ch. 9.5 - Prob. 36P Ch. 9.5 - Prob. 37P Ch. 9.5 - Prob. 38P Ch. 9.5 - Prob. 43P Ch. 9.5 - Prob. 44P Ch. 9.5 - Prob. 45P Ch. 9.5 - Prob. 46P Ch. 9.5 - CURVATURE AND TORSION 47. Circle. Show that a...Ch. 9.5 - Prob. 48P Ch. 9.5 - Prob. 49P Ch. 9.5 - Prob. 50P Ch. 9.5 - Prob. 51P Ch. 9.5 - Prob. 52P Ch. 9.5 - Prob. 53P Ch. 9.5 - Prob. 54P Ch. 9.5 - Prob. 55P Ch. 9.7 - Prob. 1P Ch. 9.7 - Prob. 2P Ch. 9.7 - Prob. 3P Ch. 9.7 - Prob. 4P Ch. 9.7 - Prob. 5P Ch. 9.7 - Prob. 6P Ch. 9.7 - Prob. 7P Ch. 9.7 - Prob. 8P Ch. 9.7 - Prob. 9P Ch. 9.7 - Prob. 10P Ch. 9.7 - Prob. 11P Ch. 9.7 - Prob. 12P Ch. 9.7 - Prob. 13P Ch. 9.7 - Prob. 14P Ch. 9.7 - Prob. 15P Ch. 9.7 - Prob. 16P Ch. 9.7 - Prob. 17P Ch. 9.7 - Prob. 18P Ch. 9.7 - Prob. 19P Ch. 9.7 - Prob. 20P Ch. 9.7 - Prob. 21P Ch. 9.7 - Prob. 22P Ch. 9.7 - Prob. 23P Ch. 9.7 - Prob. 24P Ch. 9.7 - Prob. 25P Ch. 9.7 - Prob. 26P Ch. 9.7 - Prob. 28P Ch. 9.7 - Prob. 29P Ch. 9.8 - Prob. 1P Ch. 9.8 - Prob. 2P Ch. 9.8 - Prob. 3P Ch. 9.8 - Prob. 4P Ch. 9.8 - Prob. 5P Ch. 9.8 - Prob. 6P Ch. 9.8 - Prob. 7P Ch. 9.8 - Prob. 8P Ch. 9.8 - CAS EXPERIMENT. Visualizing the Divergence. Graph...Ch. 9.8 - Prob. 11P Ch. 9.8 - Prob. 12P Ch. 9.8 - Prob. 13P Ch. 9.8 - Prob. 14P Ch. 9.8 - Prob. 15P Ch. 9.8 - Prob. 16P Ch. 9.8 - Prob. 17P Ch. 9.8 - Prob. 18P Ch. 9.8 - Prob. 19P Ch. 9.8 - Prob. 20P Ch. 9.9 - Prob. 1P Ch. 9.9 - Prob. 2P Ch. 9.9 - Prob. 3P Ch. 9.9 - Prob. 4P Ch. 9.9 - Prob. 5P Ch. 9.9 - Prob. 6P Ch. 9.9 - Prob. 7P Ch. 9.9 - Prob. 8P Ch. 9.9 - Prob. 9P Ch. 9.9 - Prob. 10P Ch. 9.9 - Prob. 11P Ch. 9.9 - Prob. 12P Ch. 9.9 - Prob. 13P Ch. 9.9 - Prob. 15P Ch. 9.9 - Prob. 16P Ch. 9.9 - Prob. 17P Ch. 9.9 - Prob. 18P Ch. 9.9 - Prob. 19P Ch. 9.9 - Prob. 20P Ch. 9 - Prob. 1RQ Ch. 9 - Prob. 2RQ Ch. 9 - Prob. 3RQ Ch. 9 - Prob. 4RQ Ch. 9 - Prob. 5RQ Ch. 9 - Prob. 6RQ Ch. 9 - Prob. 7RQ Ch. 9 - Prob. 8RQ Ch. 9 - Prob. 9RQ Ch. 9 - Prob. 11RQ Ch. 9 - Prob. 12RQ Ch. 9 - Prob. 13RQ Ch. 9 - Prob. 14RQ Ch. 9 - Prob. 15RQ Ch. 9 - Prob. 16RQ Ch. 9 - Prob. 17RQ Ch. 9 - Prob. 18RQ Ch. 9 - Prob. 19RQ Ch. 9 - Prob. 20RQ Ch. 9 - Prob. 21RQ Ch. 9 - Prob. 22RQ Ch. 9 - Prob. 23RQ Ch. 9 - Prob. 24RQ Ch. 9 - Prob. 25RQ Ch. 9 - Prob. 26RQ Ch. 9 - Prob. 27RQ Ch. 9 - Prob. 28RQ Ch. 9 - Prob. 29RQ Ch. 9 - Prob. 30RQ Ch. 9 - Prob. 31RQ Ch. 9 - Prob. 32RQ Ch. 9 - Prob. 33RQ Ch. 9 - Prob. 34RQ Ch. 9 - Prob. 35RQ Ch. 9 - Prob. 36RQ Ch. 9 - Prob. 37RQ Ch. 9 - Prob. 38RQ Ch. 9 - Prob. 39RQ Ch. 9 - Prob. 40RQ

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