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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.
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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