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Problems In Exercises 5-14, write the vector, parametric and symmet- ric equations of the lines described. 5. Passes through P = (2, -4, 1), parallel to d = (9,2,5).

Problems In Exercises 5-14, write the vector, parametric and symmet- ric equations of the lines described. 5. Passes through P = (2, -4, 1), parallel to d = (9,2,5).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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10.5) question 5
4. Use your own words to describe what it means for two lines in space to be skew. Problems In Exercises 5-14, write the vector, parametric and symmet- ric equations of the lines described. 5. Passes through P = (2, −4, 1), parallel to d = (9, 2, 5). 6. Passes through P = (6, 1,7), parallel to d = (-3, 2, 5). 7. Passes through P = (2, 1, 5) and Q = (7, -2,4). 8. Passes through P = (1, -2, 3) and Q = (5,5,5). 9. Passes through P = (0, 1, 2) and orthogonal to both d₁ = (2,-1,7) and d₂ = (7,1, 3). 10. Passes through P = (5, 1,9) and orthogonal to both d₁ = (1, 0, 1) and d₂ (2,0, 3). = 11. Passes through the point of intersection of ₁ (t) and (t) and orthogonal to both lines, where (t) = (2, 1, 1) + t (5, 1, -2) and l₂(t)= (-2,-1, 2) + t (3, 1, -1). 12. Passes through the point of intersection of l₁ (t) and ₂ (t) and orthogonal to both lines, where x=t (x=2+t l2=y= 2-t. z = 3+2t l₁ = y = −2+2t and z = 1+t 13. Passes through P = (1, 1), parallel to d = (2, 3). 14. Passes through P = (-2,5), parallel to d = (0, 1). O Search H n 20. l₁ = 21. l₁ = y Z X 22. l₁=y= 27. z = I In Exercises 23 line. 23. Q = (1, 1, 1 24. Q=(2, 5, 6) 25. Q = (0,3), 26. Q = (1, 1), In Exercises 27-2 (t) = (1, 2, 1, 2 (t)=(3,3,3) 28. ₁(t) = (0,0,1) ₂ (t) = (0,0,3) Exercises 29-31 exp las found in Key Idea
Transcribed Image Text:4. Use your own words to describe what it means for two lines in space to be skew. Problems In Exercises 5-14, write the vector, parametric and symmet- ric equations of the lines described. 5. Passes through P = (2, −4, 1), parallel to d = (9, 2, 5). 6. Passes through P = (6, 1,7), parallel to d = (-3, 2, 5). 7. Passes through P = (2, 1, 5) and Q = (7, -2,4). 8. Passes through P = (1, -2, 3) and Q = (5,5,5). 9. Passes through P = (0, 1, 2) and orthogonal to both d₁ = (2,-1,7) and d₂ = (7,1, 3). 10. Passes through P = (5, 1,9) and orthogonal to both d₁ = (1, 0, 1) and d₂ (2,0, 3). = 11. Passes through the point of intersection of ₁ (t) and (t) and orthogonal to both lines, where (t) = (2, 1, 1) + t (5, 1, -2) and l₂(t)= (-2,-1, 2) + t (3, 1, -1). 12. Passes through the point of intersection of l₁ (t) and ₂ (t) and orthogonal to both lines, where x=t (x=2+t l2=y= 2-t. z = 3+2t l₁ = y = −2+2t and z = 1+t 13. Passes through P = (1, 1), parallel to d = (2, 3). 14. Passes through P = (-2,5), parallel to d = (0, 1). O Search H n 20. l₁ = 21. l₁ = y Z X 22. l₁=y= 27. z = I In Exercises 23 line. 23. Q = (1, 1, 1 24. Q=(2, 5, 6) 25. Q = (0,3), 26. Q = (1, 1), In Exercises 27-2 (t) = (1, 2, 1, 2 (t)=(3,3,3) 28. ₁(t) = (0,0,1) ₂ (t) = (0,0,3) Exercises 29-31 exp las found in Key Idea
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