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Q3.4: NCERT Physics - Part 1 MOTION IN A PLANE 3.4 Solution: State with reasons, whether the following algebraic operations…
⚠️ Common Exam Traps & Conceptual Pitfalls
A vector component is a scalar; adding it to the vector mixes a scalar with a vector, which is dimensionally inconsistent. Only vectors of the same physical quantity can be added, and a scalar component cannot be added to its parent vector.
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful: (a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.
Step-by-Step Verified Solution
**Answer:** (a) Not meaningful in general. (b) Not meaningful. (c) Meaningful. (d) Meaningful. (e) Not meaningful in general. (f) Meaningful.
**Step-by-Step Explanation:**
(a) Adding two scalars is meaningful only if they represent the same physical quantity.
(b) A scalar cannot be added to a vector because they have different dimensions/directions.
(c) A vector can be multiplied by a scalar (e.g., force _ time = impulse). [citation:1]
(d) Two scalars can be multiplied.
(e) Adding two vectors is meaningful only if they represent the same physical quantity.
(f) A component of a vector has the same dimensions as the vector, so it can be added.
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