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(a) Let u and v be two vectors in R³ such that |u|| = 3 and ||v|| = 9. (i) Find the maximum and minimum possible values of u. v. (ii) Find the maximum and minimum possible values of ||u -- v. (b) Let u = (1, -3), v = (2,4) and w = (c,d), c, d e R, be three vectors in R2. Find all real values c, d, such that u and w are orthogonal, and vw = 3.

(a) Let u and v be two vectors in R³ such that |u|| = 3 and ||v|| = 9. (i) Find the maximum and minimum possible values of u. v. (ii) Find the maximum and minimum possible values of ||u -- v. (b) Let u = (1, -3), v = (2,4) and w = (c,d), c, d e R, be three vectors in R2. Find all real values c, d, such that u and w are orthogonal, and vw = 3.

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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Please answer the b and c part of the question. Thanks
3. (a) Let u and v be two vectors in R3 such that ||u|| = 3 and ||v|| = 9. (i) Find the maximum and minimum possible values of u. v. (ii) Find the maximum and minimum possible values of ||u -- v. (b) Let u = (1, -3), v = (2, 4) and w = (c,d), c, d e R, be three vectors in R2. Find all real values c, d, such that u and w are orthogonal, and v w = 3.
Transcribed Image Text:3. (a) Let u and v be two vectors in R3 such that ||u|| = 3 and ||v|| = 9. (i) Find the maximum and minimum possible values of u. v. (ii) Find the maximum and minimum possible values of ||u -- v. (b) Let u = (1, -3), v = (2, 4) and w = (c,d), c, d e R, be three vectors in R2. Find all real values c, d, such that u and w are orthogonal, and v w = 3.
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