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Consider a = (-1.0, 1). 6=(2,3,-1), = (4.-2,0) in R³, (a) Write down the equation of the plane, P; containing the position vectors a. b, E. mh Justify your answer.

Consider a = (-1.0, 1). 6=(2,3,-1), = (4.-2,0) in R³, (a) Write down the equation of the plane, P; containing the position vectors a. b, E. mh Justify your answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 30E
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Question 8 part a
6. Consider a = (0, 1,3),.5 = (-1,4, 2), (a) Calculate each of axb, bxc, ax (b-3a). (b) Calculate a. (bxc). (c) .Calculate Hä. |||| and a xb. Verify that a × b the angle between a and b.. 7. Consider a = (-2, 2, 1), 6=(1,1,2), = (0, 1, -3) in R³. (a) .Write down the equation of the plane,. P. containing the position vectors a, b. c. (2, 0,-1) in R³. (b) Does the point/position vector, 7=(3,-1,2) lie in P? Justify your answer, (c) Determine the value of t'e R such that (1-t, 3+ t, 2t - 1) lies in P: (8) Consider a = (-1,0,1), 6=(2,3,-1), = (4.-2,0) in R³, (a) Write down the equation of the plane, P; containing the position vectors a, b. E. (b) 'Does the point/position vector, = (1, -2, 1) lie in P? Justify your answer. (c) Determine the value of t€ R such that (t. 1-3t, t+2) lies in P. 9: Is the set 10.) Is the set. a subspace of R³2 Justify your answer. asin 0 where, 0 is S = {(1,72:23) ER³: 21 + x2 3x3 = 0} S = {A & R²x2 anan=1} a'subspace of R2x2? Justify your answer. (11.) Consider the vector space.V = P4 of polynomials of, degree at most 4. (a) 'Is the set 'S = {p € V': p(1) = 0 or p(4) = 0} a subspace of V? Justify your answer, (b) .Is the set S = {pE Vp(1) = p(4)} 'a subspace of V? Justify your answer:
Transcribed Image Text:6. Consider a = (0, 1,3),.5 = (-1,4, 2), (a) Calculate each of axb, bxc, ax (b-3a). (b) Calculate a. (bxc). (c) .Calculate Hä. |||| and a xb. Verify that a × b the angle between a and b.. 7. Consider a = (-2, 2, 1), 6=(1,1,2), = (0, 1, -3) in R³. (a) .Write down the equation of the plane,. P. containing the position vectors a, b. c. (2, 0,-1) in R³. (b) Does the point/position vector, 7=(3,-1,2) lie in P? Justify your answer, (c) Determine the value of t'e R such that (1-t, 3+ t, 2t - 1) lies in P: (8) Consider a = (-1,0,1), 6=(2,3,-1), = (4.-2,0) in R³, (a) Write down the equation of the plane, P; containing the position vectors a, b. E. (b) 'Does the point/position vector, = (1, -2, 1) lie in P? Justify your answer. (c) Determine the value of t€ R such that (t. 1-3t, t+2) lies in P. 9: Is the set 10.) Is the set. a subspace of R³2 Justify your answer. asin 0 where, 0 is S = {(1,72:23) ER³: 21 + x2 3x3 = 0} S = {A & R²x2 anan=1} a'subspace of R2x2? Justify your answer. (11.) Consider the vector space.V = P4 of polynomials of, degree at most 4. (a) 'Is the set 'S = {p € V': p(1) = 0 or p(4) = 0} a subspace of V? Justify your answer, (b) .Is the set S = {pE Vp(1) = p(4)} 'a subspace of V? Justify your answer:
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