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State, with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:1. Adding any two scalars.2. Adding a scalar to a vector of the same dimensions3. Multiplying any vector by any scalar4. Multiplying any two scalars5. Adding any two vectors6. Adding a component of a vector to the same vector. |
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Answer» 1. No. Scalars must represent same physical quantity. 2. No. Vector can be added only to another vector. 3. Yes. When a vector is multiplied by any scalar, we get a vector. 4. Yes. In multiplication, scalars may not represent the same physical quantity. 5. No. The two vectors must represent the same physical quantity. 6. Yes. The vector and its component must have the same dimensions. |
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