In three dimensional Cartesian Coordinate system (x,y,z), you have two vectors A and B. Vector A has components Ax= 4, Ay=3, and Az=2, while vector B has components Bx=1, By=5, and Bz=2. What is dot (scalar product) of vectors A and B?
Correct answer: A. 23
- A. 23
- B. -23
- C. 0
- D. 19
Explanation
To find the dot product (scalar product) of vectors A and B, you multiply the corresponding components and add them together:A · B = Ax_Bx + Ay_By + Az_Bz= (4)_(1) + (3)_(5) + (2)_(2)= 4 + 15 + 4= 23So, the correct answer is b. 23.The dot product is a scalar value that represents the amount of "similarity" between the two vectors. In this case, the result is positive, indicating that the vectors have some degree of alignment.
This question appeared on the KMU MDCAT 2023 (retake) paper, which you can sit online with every answer explained.
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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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