Properties of Scalar Product and Projection of a Vector on a Line

# Properties of Scalar Product and Projection of a Vector on a Line Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

205 videos|264 docs|139 tests

## FAQs on Properties of Scalar Product and Projection of a Vector on a Line Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is the definition of the scalar product of two vectors?
Ans. The scalar product, also known as the dot product, is an operation between two vectors that results in a scalar quantity. It is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.
 2. How is the scalar product calculated?
Ans. To calculate the scalar product of two vectors, you multiply the magnitudes of the vectors by the cosine of the angle between them. This can be represented by the formula: A · B = |A| |B| cosθ, where A and B are the vectors, |A| and |B| are their magnitudes, and θ is the angle between them.
 3. What are some properties of the scalar product?
Ans. The scalar product has several properties, including: - Commutative property: A · B = B · A - Distributive property: A · (B + C) = A · B + A · C - Scalar multiplication property: (kA) · B = k(A · B) = A · (kB), where k is a scalar - If A · B = 0, then A and B are orthogonal (perpendicular) to each other.
 4. How can the scalar product be used to determine the angle between two vectors?
Ans. The angle between two vectors can be determined using the scalar product formula. By rearranging the formula A · B = |A| |B| cosθ, you can solve for the angle θ. Taking the inverse cosine of the scalar product divided by the product of the magnitudes gives the angle: θ = cos⁻¹(A · B / (|A| |B|)).
 5. What is the projection of a vector on a line?
Ans. The projection of a vector onto a line is a vector that represents the component of the original vector that lies along the line. It is calculated by taking the scalar product of the original vector and the unit vector in the direction of the line. The formula for the projection of vector A onto a line with unit vector u is given by: projᵤA = (A · u)u.

## Mathematics (Maths) Class 12

205 videos|264 docs|139 tests

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