r₁= [3 -1 0], (a) (₁, ₂) (b) (r1,73) (c) (r2, r3) r₂ = [-2 0 1], T3 = [1 -2 4].
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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Question
please answer all parts and make sure the writing is understanable.
![Vectors:
\[ \mathbf{r_1} = [3, -1, 0] \]
\[ \mathbf{r_2} = [-2, 0, 1] \]
\[ \mathbf{r_3} = [1, -2, 4] \]
Questions:
(a) \( \langle \mathbf{r_1}, \mathbf{r_2} \rangle \)
(b) \( \langle \mathbf{r_1}, \mathbf{r_3} \rangle \)
(c) \( \langle \mathbf{r_2}, \mathbf{r_3} \rangle \)
(d) \( \mathbf{r_1} \times \mathbf{r_2} \)
(e) \( \mathbf{r_1} \times \mathbf{r_3} \)
(f) \( \mathbf{r_2} \times \mathbf{r_3} \)
(g) What is the area of the parallelogram formed by \(\mathbf{r_1}\) and \(\mathbf{r_2}\)?
(h) What is the area of the parallelogram formed by \(\mathbf{r_1}\) and \(\mathbf{r_3}\)?
(i) What is the area of the parallelogram formed by \(\mathbf{r_2}\) and \(\mathbf{r_3}\)?
(j) What is the volume of the parallelepiped formed by \(\mathbf{r_1}\), \(\mathbf{r_2}\), and \(\mathbf{r_3}\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2903bb2a-771d-40b7-a62d-703de2e08baa%2F8bad0d81-bc0a-4419-ac6c-fe146b842e29%2F9dsmts_processed.png&w=3840&q=75)
Transcribed Image Text:Vectors:
\[ \mathbf{r_1} = [3, -1, 0] \]
\[ \mathbf{r_2} = [-2, 0, 1] \]
\[ \mathbf{r_3} = [1, -2, 4] \]
Questions:
(a) \( \langle \mathbf{r_1}, \mathbf{r_2} \rangle \)
(b) \( \langle \mathbf{r_1}, \mathbf{r_3} \rangle \)
(c) \( \langle \mathbf{r_2}, \mathbf{r_3} \rangle \)
(d) \( \mathbf{r_1} \times \mathbf{r_2} \)
(e) \( \mathbf{r_1} \times \mathbf{r_3} \)
(f) \( \mathbf{r_2} \times \mathbf{r_3} \)
(g) What is the area of the parallelogram formed by \(\mathbf{r_1}\) and \(\mathbf{r_2}\)?
(h) What is the area of the parallelogram formed by \(\mathbf{r_1}\) and \(\mathbf{r_3}\)?
(i) What is the area of the parallelogram formed by \(\mathbf{r_2}\) and \(\mathbf{r_3}\)?
(j) What is the volume of the parallelepiped formed by \(\mathbf{r_1}\), \(\mathbf{r_2}\), and \(\mathbf{r_3}\)?
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