Which among the statements below are correct about the vectors?i. Each vector may not have a vector representation at times.ii. Vectors can either be represented by an arrow or by component.iii. Equivalent vectors have the same magnitude and the same direction while equal vectors have the same magnitude.iv. There are two ways to perform multiplication on vectors: scalar product and vector product.Group of answer choicesi and iiiii and ivi and iiiii and iv
Question
Which among the statements below are correct about the vectors?i. Each vector may not have a vector representation at times.ii. Vectors can either be represented by an arrow or by component.iii. Equivalent vectors have the same magnitude and the same direction while equal vectors have the same magnitude.iv. There are two ways to perform multiplication on vectors: scalar product and vector product.Group of answer choicesi and iiiii and ivi and iiiii and iv
Solution
The correct answer is ii and iv.
Explanation:
ii. Vectors can either be represented by an arrow or by component. This is correct. A vector can be represented graphically as an arrow, where the length represents the magnitude and the direction of the arrow represents the direction. Alternatively, a vector can be represented by its components, which are the projections of the vector along the coordinate axes.
iv. There are two ways to perform multiplication on vectors: scalar product and vector product. This is also correct. The scalar product (also known as the dot product) results in a scalar, while the vector product (also known as the cross product) results in a new vector.
i. Each vector may not have a vector representation at times. This is incorrect. Every vector has a vector representation, either graphically or as components.
iii. Equivalent vectors have the same magnitude and the same direction while equal vectors have the same magnitude. This is incorrect. Equivalent vectors and equal vectors both have the same magnitude and direction. The difference is that equivalent vectors can start at different points in space, while equal vectors also have the same initial point.
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