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Extended Answer Question 1 (a) Let A = (2,0, -1), B = (0, 4, -1) and C = (1, 2, 0) be points in R³. (i) Find a general form of the equation for the plane P containing A, B and C. (ii) Find parametric equations for the line that passes through B and is parallel to the vector AC AC (b) Br

Extended Answer Question 1 (a) Let A = (2,0, -1), B = (0, 4, -1) and C = (1, 2, 0) be points in R³. (i) Find a general form of the equation for the plane P containing A, B and C. (ii) Find parametric equations for the line that passes through B and is parallel to the vector AC AC (b) Br

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Extended Answer Question 1 (a) Let A = (2, 0, -1), B = (0, 4, -1) and C= (1, 2, 0) be points in R³. (i) Find a general form of the equation for the plane P containing A, B and C. (ii) Find parametric equations for the line that passes through B and is parallel to the vector AC. (b) Prove that for all vectors v and w in R", ||vw||² = ||v||² + ||w||² -2(vw) At each step in your proof, you should name or state the property of the dot product that you are using. (c) Now let v and w be vectors in R3 and suppose that ||v|| = 4, ||w|| = 5 and w|| = 7. (i) Use the result of part (b) to compute v . w. (ii) Use the value of v w you found in part (c)(i) to compute ||vxw|. Give your answer as an exact value.
Transcribed Image Text:Extended Answer Question 1 (a) Let A = (2, 0, -1), B = (0, 4, -1) and C= (1, 2, 0) be points in R³. (i) Find a general form of the equation for the plane P containing A, B and C. (ii) Find parametric equations for the line that passes through B and is parallel to the vector AC. (b) Prove that for all vectors v and w in R", ||vw||² = ||v||² + ||w||² -2(vw) At each step in your proof, you should name or state the property of the dot product that you are using. (c) Now let v and w be vectors in R3 and suppose that ||v|| = 4, ||w|| = 5 and w|| = 7. (i) Use the result of part (b) to compute v . w. (ii) Use the value of v w you found in part (c)(i) to compute ||vxw|. Give your answer as an exact value.
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