The following vector-valued function defines a line in three dimensions L(t) = (21,2+1,6-t)= 2ti + (2+t)j+(6-t)k. 4. Give a direction vector for this line. At what point does this line intersect the xy-plane? А. B.
The following vector-valued function defines a line in three dimensions L(t) = (21,2+1,6-t)= 2ti + (2+t)j+(6-t)k. 4. Give a direction vector for this line. At what point does this line intersect the xy-plane? А. B.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Make all obvious simplifications.
![**Vector-Valued Function for a Line in Three Dimensions**
The following vector-valued function defines a line in three dimensions:
\[ \mathbf{L}(t) = \langle 2t, 2+t, 6-t \rangle = 2t\mathbf{i} + (2+t)\mathbf{j} + (6-t)\mathbf{k} \]
**Tasks:**
A. **Direction Vector:**
Identify the direction vector for this line.
B. **Intersection with the xy-plane:**
Determine the point at which this line intersects the xy-plane.
To solve these problems, analyze the given vector equation. The direction vector can be extracted from the coefficients of \(t\). For the intersection with the xy-plane, find when the \(z\)-component equals zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c560a1a-db76-4fd0-82f5-78bd443b8157%2Ff00da3c3-31d7-4b11-9a8e-5182fbfaa907%2Fc63un8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vector-Valued Function for a Line in Three Dimensions**
The following vector-valued function defines a line in three dimensions:
\[ \mathbf{L}(t) = \langle 2t, 2+t, 6-t \rangle = 2t\mathbf{i} + (2+t)\mathbf{j} + (6-t)\mathbf{k} \]
**Tasks:**
A. **Direction Vector:**
Identify the direction vector for this line.
B. **Intersection with the xy-plane:**
Determine the point at which this line intersects the xy-plane.
To solve these problems, analyze the given vector equation. The direction vector can be extracted from the coefficients of \(t\). For the intersection with the xy-plane, find when the \(z\)-component equals zero.
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