Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors u = - 6i + 7j + 7k and v = - 5i + 4j -7k. O A. x= -77t-5 y = 77t+ 6 Z= 11t + 7 O B. x= - 77t + 5 y = -77t-6 Z= - 7t-7 O D. x= - 77t-5 y = - 77t+6 Z = 11t +7 O C. x=-77t-5 y= - 77t+6 Z= - 7t+7
Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors u = - 6i + 7j + 7k and v = - 5i + 4j -7k. O A. x= -77t-5 y = 77t+ 6 Z= 11t + 7 O B. x= - 77t + 5 y = -77t-6 Z= - 7t-7 O D. x= - 77t-5 y = - 77t+6 Z = 11t +7 O C. x=-77t-5 y= - 77t+6 Z= - 7t+7
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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![**Title: Finding Parametric Equations of a Line Perpendicular to Given Vectors**
**Task:**
Find parametric equations for the line through the point \( P(-5, 6, 7) \) and perpendicular to the vectors \( \mathbf{u} = -6\mathbf{i} + 7\mathbf{j} + 7\mathbf{k} \) and \( \mathbf{v} = -5\mathbf{i} + 4\mathbf{j} - 7\mathbf{k} \).
**Options:**
- **A:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= 77t + 6 \\
z &= 11t + 7 \\
\end{align*}
\]
- **B:**
\[
\begin{align*}
x &= -77t + 5 \\
y &= -77t - 6 \\
z &= -7t - 7 \\
\end{align*}
\]
- **C:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= -77t + 6 \\
z &= -7t + 7 \\
\end{align*}
\]
- **D:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= -77t + 6 \\
z &= 11t + 7 \\
\end{align*}
\]
**Explanation:**
To construct the parametric equations of the line that passes through a point and is perpendicular to two vectors, we need to find the cross product of the two vectors to obtain a direction vector for the line. Then, using the point given, we can write the parametric equations utilizing this direction vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c62ea9-2423-4a35-a6cd-74646c6bbd41%2F9f5a0879-db86-4159-a533-c8b5a1b842cf%2F7dpxj4d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding Parametric Equations of a Line Perpendicular to Given Vectors**
**Task:**
Find parametric equations for the line through the point \( P(-5, 6, 7) \) and perpendicular to the vectors \( \mathbf{u} = -6\mathbf{i} + 7\mathbf{j} + 7\mathbf{k} \) and \( \mathbf{v} = -5\mathbf{i} + 4\mathbf{j} - 7\mathbf{k} \).
**Options:**
- **A:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= 77t + 6 \\
z &= 11t + 7 \\
\end{align*}
\]
- **B:**
\[
\begin{align*}
x &= -77t + 5 \\
y &= -77t - 6 \\
z &= -7t - 7 \\
\end{align*}
\]
- **C:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= -77t + 6 \\
z &= -7t + 7 \\
\end{align*}
\]
- **D:**
\[
\begin{align*}
x &= -77t - 5 \\
y &= -77t + 6 \\
z &= 11t + 7 \\
\end{align*}
\]
**Explanation:**
To construct the parametric equations of the line that passes through a point and is perpendicular to two vectors, we need to find the cross product of the two vectors to obtain a direction vector for the line. Then, using the point given, we can write the parametric equations utilizing this direction vector.
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