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The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ?
a. π/2
b. cos -1 (0.6)
c. tan -1 (7/5)
d. π/4?
a. π/2
b. cos -1 (0.6)
c. tan -1 (7/5)
d. π/4?
Most Upvoted Answer
The magnitude of vector A B and C are 3 4 and 5 units respectively. if...
Given Information
The magnitudes of vectors A, B, and C are:
- |A| = 3 units
- |B| = 4 units
- |C| = 5 units
It is given that vector A + vector B = vector C.
Using the Law of Cosines
To find the angle θ between vectors A and B, we can apply the Law of Cosines, which states:
\[ |C|^2 = |A|^2 + |B|^2 - 2|A||B|\cos(θ) \]
Substituting the known values:
\[ 5^2 = 3^2 + 4^2 - 2 \cdot 3 \cdot 4 \cdot \cos(θ) \]
This simplifies to:
\[ 25 = 9 + 16 - 24\cos(θ) \]
\[ 25 = 25 - 24\cos(θ) \]
Thus, we can rearrange the equation:
\[ 0 = -24\cos(θ) \]
This implies:
\[ \cos(θ) = 0 \]
Determining the Angle
The angle θ for which the cosine is zero is:
- θ = π/2 radians (or 90 degrees)
Conclusion
The angle between vectors A and B is:
- **a. π/2**
This indicates that vectors A and B are perpendicular to each other.
The magnitudes of vectors A, B, and C are:
- |A| = 3 units
- |B| = 4 units
- |C| = 5 units
It is given that vector A + vector B = vector C.
Using the Law of Cosines
To find the angle θ between vectors A and B, we can apply the Law of Cosines, which states:
\[ |C|^2 = |A|^2 + |B|^2 - 2|A||B|\cos(θ) \]
Substituting the known values:
\[ 5^2 = 3^2 + 4^2 - 2 \cdot 3 \cdot 4 \cdot \cos(θ) \]
This simplifies to:
\[ 25 = 9 + 16 - 24\cos(θ) \]
\[ 25 = 25 - 24\cos(θ) \]
Thus, we can rearrange the equation:
\[ 0 = -24\cos(θ) \]
This implies:
\[ \cos(θ) = 0 \]
Determining the Angle
The angle θ for which the cosine is zero is:
- θ = π/2 radians (or 90 degrees)
Conclusion
The angle between vectors A and B is:
- **a. π/2**
This indicates that vectors A and B are perpendicular to each other.
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The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4?
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The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4?.
The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of vector A B and C are 3 4 and 5 units respectively. if A and B vector is equal to C vector , the angle between A and B vector is ? a. π/2b. cos -1 (0.6)c. tan -1 (7/5)d. π/4?.
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