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a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors
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a vector of magnitude 100 and is inclined at an angle of 30 degree to ...
Introduction:
In this problem, we are given two vectors: Vector A with a magnitude of 100 and Vector B with a magnitude of 50. Vector A is inclined at an angle of 30 degrees to Vector B. We need to calculate the magnitude of the dot product and the cross product of these two vectors.
Dot Product:
The dot product, also known as the scalar product, of two vectors A and B is a scalar value obtained by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The formula for the dot product is:
A · B = |A| |B| cosθ
Where:
- A · B represents the dot product of vectors A and B
- |A| and |B| represent the magnitudes of vectors A and B, respectively
- θ represents the angle between vectors A and B
Magnitude of the Dot Product:
In this case, we have Vector A with a magnitude of 100 and Vector B with a magnitude of 50. The angle between them is 30 degrees. Plugging these values into the formula, we get:
A · B = 100 * 50 * cos(30°) = 5000 * 0.866 = 4330
Therefore, the magnitude of the dot product of Vector A and Vector B is 4330.
Cross Product:
The cross product, also known as the vector product, of two vectors A and B is a vector that is perpendicular to both A and B. The magnitude of the cross product is given by:
|A x B| = |A| |B| sinθ
Where:
- A x B represents the cross product of vectors A and B
- |A| and |B| represent the magnitudes of vectors A and B, respectively
- θ represents the angle between vectors A and B
Magnitude of the Cross Product:
In this case, to calculate the cross product, we need to determine the direction of the resultant vector. Since the angle between Vector A and Vector B is 30 degrees, and Vector A is inclined to Vector B, the cross product will be perpendicular to the plane containing both vectors. The magnitude of the cross product is given by:
|A x B| = |A| |B| sin(θ) = 100 * 50 * sin(30°) = 5000 * 0.5 = 2500
Therefore, the magnitude of the cross product of Vector A and Vector B is 2500.
Summary:
- The magnitude of the dot product of Vector A and Vector B is 4330.
- The magnitude of the cross product of Vector A and Vector B is 2500.
- The dot product is a scalar value, while the cross product is a vector.
- The dot product measures the similarity or projection of one vector onto another.
- The cross product measures the perpendicularity or the creation of a new vector perpendicular to both input vectors.
In this problem, we are given two vectors: Vector A with a magnitude of 100 and Vector B with a magnitude of 50. Vector A is inclined at an angle of 30 degrees to Vector B. We need to calculate the magnitude of the dot product and the cross product of these two vectors.
Dot Product:
The dot product, also known as the scalar product, of two vectors A and B is a scalar value obtained by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The formula for the dot product is:
A · B = |A| |B| cosθ
Where:
- A · B represents the dot product of vectors A and B
- |A| and |B| represent the magnitudes of vectors A and B, respectively
- θ represents the angle between vectors A and B
Magnitude of the Dot Product:
In this case, we have Vector A with a magnitude of 100 and Vector B with a magnitude of 50. The angle between them is 30 degrees. Plugging these values into the formula, we get:
A · B = 100 * 50 * cos(30°) = 5000 * 0.866 = 4330
Therefore, the magnitude of the dot product of Vector A and Vector B is 4330.
Cross Product:
The cross product, also known as the vector product, of two vectors A and B is a vector that is perpendicular to both A and B. The magnitude of the cross product is given by:
|A x B| = |A| |B| sinθ
Where:
- A x B represents the cross product of vectors A and B
- |A| and |B| represent the magnitudes of vectors A and B, respectively
- θ represents the angle between vectors A and B
Magnitude of the Cross Product:
In this case, to calculate the cross product, we need to determine the direction of the resultant vector. Since the angle between Vector A and Vector B is 30 degrees, and Vector A is inclined to Vector B, the cross product will be perpendicular to the plane containing both vectors. The magnitude of the cross product is given by:
|A x B| = |A| |B| sin(θ) = 100 * 50 * sin(30°) = 5000 * 0.5 = 2500
Therefore, the magnitude of the cross product of Vector A and Vector B is 2500.
Summary:
- The magnitude of the dot product of Vector A and Vector B is 4330.
- The magnitude of the cross product of Vector A and Vector B is 2500.
- The dot product is a scalar value, while the cross product is a vector.
- The dot product measures the similarity or projection of one vector onto another.
- The cross product measures the perpendicularity or the creation of a new vector perpendicular to both input vectors.
Community Answer
a vector of magnitude 100 and is inclined at an angle of 30 degree to ...
2500√3 and 2500 respectively
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a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors
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a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors.
a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a vector of magnitude 100 and is inclined at an angle of 30 degree to another vector of magnitude 50 and calculate magnitude of dot product and cross product of two vectors.
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