Question

 Choose the WRONG statement

1) The division of vector by scalar is valid.

2) The multiplication of vector by scalar is valid.

3) The multiplication of vector by another vector is valid by using vector algebra.

4) The division of vector by another vector is valid by using vector algebra.​

Answer 1

(a) Yes, addition of two scalar quantities is meaningful only if they both represent the same physical quantity.

(b) No, addition of a vector quantity with a scalar quantity is not meaningful.

(c) Yes, scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.

(d) Yes, scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.

(e) Yes, addition of two vector quantities is meaningful only if they both represent the same physical quantity.

(f) Yes, component of a vector can be added to the same vector as they both have the same dimensions.

Explanation:

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Answer 2

Wrong statement is 4) The division of vector any another vector is valid by using vector algebra.

Explanation:

1. Division of vector with scalar is valid. It is same as multiplying reciprocal of the scalar number with the vector. Result is a vector quantity.
2. Multiplication of vector by scalar is also valid. Result is a vector quantity. The magnitude of vector is multiplied with scalar and the direction remains same as the vector.
3. Multiplication of a vector is valid with another vector. It is of two types: One is dot product and other is cross product. Dot product of two vectors give a scalar quantity whereas cross product of two vectors give vector quantity. The direction is of resultant cross product is perpendicular to both the vectors that was multiplied.
4. Division of vector by another vector is not valid. Because division of two directions does not make sense.