For the vectors A equals 2i + 3j and B equals 4i minus j, the scalar product A dot B is
Correct answer: B. 5
- A. 11
- B. 5
- C. 8
- D. minus 3
Explanation
In component form the dot product is the sum of the products of like components, so (2)(4) plus (3)(minus 1) gives 8 minus 3, which is 5. Only i with i and j with j contribute, because the unit vectors along different axes are perpendicular and their dot products vanish. The value 8 is the first term alone and 11 comes from adding rather than subtracting.
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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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