Use a calculator to find the angle between the planes 8x - 9y +6z = -3 and -9x - 5y +5z = -2 to the nearest thousandth of a radian. O 1.551 rad 0.303 rad O 1.538 rad O 0.019 rad
Use a calculator to find the angle between the planes 8x - 9y +6z = -3 and -9x - 5y +5z = -2 to the nearest thousandth of a radian. O 1.551 rad 0.303 rad O 1.538 rad O 0.019 rad
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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![### Calculating the Angle Between Two Planes
**Problem Statement:**
Use a calculator to find the angle between the planes \( 8x - 9y + 6z = -3 \) and \( -9x - 5y + 5z = -2 \) to the nearest thousandth of a radian.
**Options:**
- ( ) 1.551 rad
- ( ) 0.303 rad
- ( ) 1.538 rad
- ( ) 0.019 rad
To solve this problem, you will need to use the formula for the angle between two planes. The angle \( \theta \) between the planes can be found using the dot product of their normal vectors \( \vec{n_1} \) and \( \vec{n_2} \):
\[
\cos \theta = \frac{\vec{n_1} \cdot \vec{n_2}}{||\vec{n_1}|| \cdot ||\vec{n_2}||}
\]
Where:
\(\vec{n_1} = \langle 8, -9, 6 \rangle\) and \(\vec{n_2} = \langle -9, -5, 5 \rangle\).
Using the dot product and magnitudes of these vectors, you can compute \( \theta \) and choose the correct answer from the provided options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86779032-2cf1-4d1b-9093-232d60baa1f8%2Ff7750f04-60ab-48ed-96b6-aa094b05a105%2F11idkz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating the Angle Between Two Planes
**Problem Statement:**
Use a calculator to find the angle between the planes \( 8x - 9y + 6z = -3 \) and \( -9x - 5y + 5z = -2 \) to the nearest thousandth of a radian.
**Options:**
- ( ) 1.551 rad
- ( ) 0.303 rad
- ( ) 1.538 rad
- ( ) 0.019 rad
To solve this problem, you will need to use the formula for the angle between two planes. The angle \( \theta \) between the planes can be found using the dot product of their normal vectors \( \vec{n_1} \) and \( \vec{n_2} \):
\[
\cos \theta = \frac{\vec{n_1} \cdot \vec{n_2}}{||\vec{n_1}|| \cdot ||\vec{n_2}||}
\]
Where:
\(\vec{n_1} = \langle 8, -9, 6 \rangle\) and \(\vec{n_2} = \langle -9, -5, 5 \rangle\).
Using the dot product and magnitudes of these vectors, you can compute \( \theta \) and choose the correct answer from the provided options.
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