Find the value of a so that vectors U = ai + 6j and V = 3i+ 15j are perpendicular. a = -90 X Need Help? Read It Watch It M
Find the value of a so that vectors U = ai + 6j and V = 3i+ 15j are perpendicular. a = -90 X Need Help? Read It Watch It M
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°.
Related questions
Question
Section 7.6 question 13
![### Understanding Perpendicular Vectors
In this lesson, we'll explore how to find the value of a parameter that makes two vectors perpendicular. Perpendicular vectors have a dot product equal to zero.
#### Problem Statement:
Given two vectors:
- \( \mathbf{U} = ai + 6j \)
- \( \mathbf{V} = 3i + 15j \)
Find the value of \( a \) such that these vectors are perpendicular.
#### Solution:
To determine the value of \( a \) that makes vectors \( \mathbf{U} \) and \( \mathbf{V} \) perpendicular, we need to use the dot product formula:
\[ \mathbf{U} \cdot \mathbf{V} = (ai + 6j) \cdot (3i + 15j) \]
The dot product of two vectors \( \mathbf{U} \) and \( \mathbf{V} \) is calculated as:
\[ \mathbf{U} \cdot \mathbf{V} = (a \cdot 3) + (6 \cdot 15) \]
To simplify, we get:
\[ 3a + 90 \]
For the vectors to be perpendicular, their dot product must equal zero:
\[ 3a + 90 = 0 \]
Solving for \( a \):
\[ 3a = -90 \]
\[ a = -30 \]
Thus, the value of \( a \) that makes the vectors perpendicular is:
\[ a = -30 \]
#### Visual Summary:
This example teaches you how to find the value of a parameter that ensures two given vectors are perpendicular by using the dot product formula.
#### Reference:
In the context of the problem, note that the result \( a = -90 \) indicated an incorrect solution. The corrected solution provided above \( (a = -30) \) is based on properly solving the provided equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29eaf221-c72e-4b9c-a681-25e14c4a1cc7%2F192e10f9-e0d1-4152-926e-e1129384a1b7%2Fa18603_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Perpendicular Vectors
In this lesson, we'll explore how to find the value of a parameter that makes two vectors perpendicular. Perpendicular vectors have a dot product equal to zero.
#### Problem Statement:
Given two vectors:
- \( \mathbf{U} = ai + 6j \)
- \( \mathbf{V} = 3i + 15j \)
Find the value of \( a \) such that these vectors are perpendicular.
#### Solution:
To determine the value of \( a \) that makes vectors \( \mathbf{U} \) and \( \mathbf{V} \) perpendicular, we need to use the dot product formula:
\[ \mathbf{U} \cdot \mathbf{V} = (ai + 6j) \cdot (3i + 15j) \]
The dot product of two vectors \( \mathbf{U} \) and \( \mathbf{V} \) is calculated as:
\[ \mathbf{U} \cdot \mathbf{V} = (a \cdot 3) + (6 \cdot 15) \]
To simplify, we get:
\[ 3a + 90 \]
For the vectors to be perpendicular, their dot product must equal zero:
\[ 3a + 90 = 0 \]
Solving for \( a \):
\[ 3a = -90 \]
\[ a = -30 \]
Thus, the value of \( a \) that makes the vectors perpendicular is:
\[ a = -30 \]
#### Visual Summary:
This example teaches you how to find the value of a parameter that ensures two given vectors are perpendicular by using the dot product formula.
#### Reference:
In the context of the problem, note that the result \( a = -90 \) indicated an incorrect solution. The corrected solution provided above \( (a = -30) \) is based on properly solving the provided equations.
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