Class 11 Exam > Class 11 Questions > If the resultant of the vectors 3i cap +4jcap...
Start Learning for Free
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta?
Most Upvoted Answer
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + ...
Understanding the Vectors
To find the cosine of the angle θ that the resultant vector makes with the x-axis, we first need to determine the resultant vector from the two given vectors:
1. Vector A: 3i + 4j + 5k
2. Vector B: 5i + 3j + 4k
Calculating the Resultant Vector
- The resultant vector R is obtained by adding the corresponding components of the two vectors:
R = (3i + 5i) + (4j + 3j) + (5k + 4k)
R = (8i + 7j + 9k)
Finding the Magnitude of the Resultant Vector
- The magnitude of vector R can be calculated using the formula:
|R| = √(8² + 7² + 9²)
|R| = √(64 + 49 + 81)
|R| = √194
Calculating the Cosine of the Angle θ
- The cosine of the angle θ with respect to the x-axis is given by the formula:
cos(θ) = (Component along x-axis) / |R|
cos(θ) = 8 / √194
Final Expression
Thus, the expression for cos(θ) is:
- cos(θ) = 8 / √194
This value indicates how much the resultant vector aligns with the x-axis. A higher value indicates a stronger alignment with the x-axis, while a lower value indicates less alignment.
To find the cosine of the angle θ that the resultant vector makes with the x-axis, we first need to determine the resultant vector from the two given vectors:
1. Vector A: 3i + 4j + 5k
2. Vector B: 5i + 3j + 4k
Calculating the Resultant Vector
- The resultant vector R is obtained by adding the corresponding components of the two vectors:
R = (3i + 5i) + (4j + 3j) + (5k + 4k)
R = (8i + 7j + 9k)
Finding the Magnitude of the Resultant Vector
- The magnitude of vector R can be calculated using the formula:
|R| = √(8² + 7² + 9²)
|R| = √(64 + 49 + 81)
|R| = √194
Calculating the Cosine of the Angle θ
- The cosine of the angle θ with respect to the x-axis is given by the formula:
cos(θ) = (Component along x-axis) / |R|
cos(θ) = 8 / √194
Final Expression
Thus, the expression for cos(θ) is:
- cos(θ) = 8 / √194
This value indicates how much the resultant vector aligns with the x-axis. A higher value indicates a stronger alignment with the x-axis, while a lower value indicates less alignment.
Community Answer
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + ...
Is the answer is near about 0.574 ??
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta?
Question Description
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta?.
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta?.
Solutions for If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? defined & explained in the simplest way possible. Besides giving the explanation of
If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta?, a detailed solution for If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? has been provided alongside types of If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? theory, EduRev gives you an
ample number of questions to practice If the resultant of the vectors 3i cap +4jcap+5kcap and 5icap+3jcap + 4 kcapvmakes an angle theeta with x axis then find cos theeta? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup