If the scalar product of two unit vectors is one (i-i= 1), then both vectors will be
Correct answer: A. Parallel vectors
- A. Parallel vectors
- B. In any direction.
- C. Antiparallel vectors
- D. Perpendicular to each other.
Explanation
The scalar product or dot product of two vectors is given by a · b = |a||b|cosθ, where θ is the angle between the vectors. If both vectors are unit vectors, |a| = |b| = 1. Therefore, the dot product simplifies to cosθ = 1, which implies θ = 0 degrees. This means the vectors are parallel and point in the same direction. Option A is correct. Option B is incorrect because vectors in any direction do not guarantee a dot product of 1. Option C is incorrect because antiparallel vectors have a dot product of -1. Option D is incorrect because perpendicular vectors have a dot product of 0.
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About Scalar Product
The scalar product of two vectors is A dot B equals AB cos theta, producing a scalar determined by their magnitudes and included angle. Applications include work done and projection of one vector on another, with perpendicular vectors giving zero and the scalar product distinguished from the vector product.
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