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Scalar (or Dot) Product of 2 Vectors Video Lecture | Mathematics (Maths) Class 12 - JEE

205 videos|264 docs|139 tests

FAQs on Scalar (or Dot) Product of 2 Vectors Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the formula for calculating the scalar (or dot) product of two vectors?
Ans. The formula for calculating the scalar (or dot) product of two vectors A and B is given by: A · B = |A| |B| cosθ, where |A| and |B| represent the magnitudes of the vectors, and θ is the angle between them.
2. How do I determine the angle between two vectors in order to calculate their dot product?
Ans. To determine the angle between two vectors A and B, you can use the formula: cosθ = (A · B) / (|A| |B|), where A · B is the dot product of the vectors and |A| and |B| are their magnitudes. By rearranging the formula, you can solve for θ.
3. What does the result of the dot product of two vectors represent?
Ans. The result of the dot product of two vectors represents the magnitude of one vector projected onto the other vector, multiplied by the magnitude of the second vector. It provides a measure of the similarity or alignment between the two vectors.
4. Can the dot product of two vectors be negative?
Ans. Yes, the dot product of two vectors can be negative. This occurs when the angle between the vectors is greater than 90 degrees, indicating that they are pointing in opposite directions or have a significant misalignment. A positive dot product indicates alignment, while a negative dot product indicates anti-alignment.
5. How is the dot product related to vector projection?
Ans. The dot product is related to vector projection as it provides a way to calculate the magnitude of one vector projected onto another vector. By dividing the dot product by the magnitude of the second vector, you can determine the length of the projection of the first vector onto the second vector.
205 videos|264 docs|139 tests
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