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Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ?
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Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF T...
Given Information:
- Magnitude of vector A = 2 units
- Magnitude of vector B = 4 units
- Angle between vectors A and B = 120 degrees
Finding Vector A:
To find vector A, we can use the formula for the dot product of two vectors:
A • B = |A| * |B| * cos(θ)
where A • B is the dot product of vectors A and B, |A| and |B| are the magnitudes of vectors A and B respectively, and θ is the angle between the two vectors.
Given that |A| = 2 units, |B| = 4 units, and θ = 120 degrees, we can plug these values into the formula:
2 * 4 * cos(120) = A • B
8 * (-0.5) = A • B
A • B = -4
Calculating Vector A:
To find vector A, we need to determine its direction. The dot product of two vectors is given by:
A • B = |A| * |B| * cos(θ)
A • B = |A| * |B| * cos(120)
A • B = 2 * 4 * (-0.5)
A • B = -4
Since A • B = -4, the vectors A and B are anti-parallel. This means that vector A is in the opposite direction of vector B.
Result:
Therefore, vector A has a magnitude of 2 units and is in the opposite direction of vector B.
- Magnitude of vector A = 2 units
- Magnitude of vector B = 4 units
- Angle between vectors A and B = 120 degrees
Finding Vector A:
To find vector A, we can use the formula for the dot product of two vectors:
A • B = |A| * |B| * cos(θ)
where A • B is the dot product of vectors A and B, |A| and |B| are the magnitudes of vectors A and B respectively, and θ is the angle between the two vectors.
Given that |A| = 2 units, |B| = 4 units, and θ = 120 degrees, we can plug these values into the formula:
2 * 4 * cos(120) = A • B
8 * (-0.5) = A • B
A • B = -4
Calculating Vector A:
To find vector A, we need to determine its direction. The dot product of two vectors is given by:
A • B = |A| * |B| * cos(θ)
A • B = |A| * |B| * cos(120)
A • B = 2 * 4 * (-0.5)
A • B = -4
Since A • B = -4, the vectors A and B are anti-parallel. This means that vector A is in the opposite direction of vector B.
Result:
Therefore, vector A has a magnitude of 2 units and is in the opposite direction of vector B.
Community Answer
Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF T...
A.B = mag of A * mag of B * cosΦ
= 2*4*-1/2=-4 is the ans
= 2*4*-1/2=-4 is the ans
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Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ?
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Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ? 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 Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ?.
Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ? 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 Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vectors A and B have magnitude 2 units and 4 units. Find A. B IF THE ANGLE BETWEEN THEM IS 120 degree ?.
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