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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?
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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 ??
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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?
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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?.
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