consider having a force will you need 100 LB box то apply on to a a 75incline hold How the box in place? much horizontal
consider having a force will you need 100 LB box то apply on to a a 75incline hold How the box in place? much horizontal
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question 9
![Certainly!
---
### Orthogonality of Vectors
To determine if two vectors are orthogonal (perpendicular to each other), you need to check if their dot product is zero.
**Example:**
Given vectors \( \mathbf{u} = \langle 5, 8 \rangle \) and \( \mathbf{v} = \langle 16, -10 \rangle \), see if they are orthogonal:
\[ \mathbf{u} \cdot \mathbf{v} = (5)(16) + (8)(-10) = 80 - 80 = 0 \]
Since the dot product is zero, the vectors are orthogonal.
---
### Problem 9: Inclined Plane Force Calculation
Consider having a 100 lb box on a 75° incline. How much horizontal force will you need to apply to hold the box in place?
To find the required horizontal force, calculate the component of the gravitational force parallel to the incline and then find the horizontal component using trigonometric functions.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F085e24e4-6db3-44bd-bedd-407e7fcd33ea%2F604f5639-9452-4562-a3c4-da1c06aba310%2F6rcbjbk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly!
---
### Orthogonality of Vectors
To determine if two vectors are orthogonal (perpendicular to each other), you need to check if their dot product is zero.
**Example:**
Given vectors \( \mathbf{u} = \langle 5, 8 \rangle \) and \( \mathbf{v} = \langle 16, -10 \rangle \), see if they are orthogonal:
\[ \mathbf{u} \cdot \mathbf{v} = (5)(16) + (8)(-10) = 80 - 80 = 0 \]
Since the dot product is zero, the vectors are orthogonal.
---
### Problem 9: Inclined Plane Force Calculation
Consider having a 100 lb box on a 75° incline. How much horizontal force will you need to apply to hold the box in place?
To find the required horizontal force, calculate the component of the gravitational force parallel to the incline and then find the horizontal component using trigonometric functions.
---
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