The scalar product of (2i - j + 3k).(3i + 2j - k)?
Correct answer: A. 1
- A. 1
- B. 2
- C. 10
- D. 20
- E. 25
Explanation
The scalar product (also known as the dot product) of two vectors is calculated by multiplying their corresponding components and adding the results: (2i-j+3k) • (3i+2j-k) = 2×3 + (-1)×2 + 3×(-1) = 6 - 2 - 3 = 1. Options B, C, D, and E are incorrect as they result from miscalculations in either the component multiplication or the addition of these products.
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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