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Let P = (0, 1, 0), Q = (0, 0, 2), and O a vector of the form w = t₁oP+t₂00 linear combination of OP and O. What can you llowing assumptions? 1 + t₂ = 1? ¹ +t2 = 1 and t₁ ≥ 0? ≥ 0, t₂ ≥ 0 and t₁ + t₂ ≤ 1? ine passing through P and Q can be described by OP+tPQ=OP+t(OQ - OP).

Let P = (0, 1, 0), Q = (0, 0, 2), and O a vector of the form w = t₁oP+t₂00 linear combination of OP and O. What can you llowing assumptions? 1 + t₂ = 1? ¹ +t2 = 1 and t₁ ≥ 0? ≥ 0, t₂ ≥ 0 and t₁ + t₂ ≤ 1? ine passing through P and Q can be described by OP+tPQ=OP+t(OQ - OP).

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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Let P = (0, 1, 0), Q Recall that a vector of the form = w = t₁OP+t₂00 (0, 0, 2), and O = (0, 0, 0). is called the linear combination of OP and O. What can you say about w under the following assumptions? If t₁ + t2 = 1? ¹ If t₁ + t₂ = 1 and t₁ ≥ 0? If t₁ ≥ 0, t₂ ≥ 0 and t₁ + t2 ≤ 1? Hint: the line passing through P and Q can be described by OP + tPQ = OP + t(OQ – OỈ).
Transcribed Image Text:Let P = (0, 1, 0), Q Recall that a vector of the form = w = t₁OP+t₂00 (0, 0, 2), and O = (0, 0, 0). is called the linear combination of OP and O. What can you say about w under the following assumptions? If t₁ + t2 = 1? ¹ If t₁ + t₂ = 1 and t₁ ≥ 0? If t₁ ≥ 0, t₂ ≥ 0 and t₁ + t2 ≤ 1? Hint: the line passing through P and Q can be described by OP + tPQ = OP + t(OQ – OỈ).
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