Question

how much will change if the point moves from a distance of units in the direction ? enter a positive or negative number with exactly two decimal place

Answer 1

The change in position, when the point moves a distance of d units in the direction of
`\(\mathbf{v}\)`, is -d units.

Step-by-step explanation:

When a point moves in a certain direction, the change in position is determined by both the distance moved and the direction of the movement. In this case, the point is moving d units in the direction of vector
`\(\mathbf{v}\)`. The negative sign in the answer indicates that the change is in the opposite direction to
`\(\mathbf{v}\)`.

To elaborate, let's consider a vector
`\(\mathbf{v}\)` with magnitude
`\(|\mathbf{v}|\)`and direction given by the unit vector
`\(\hat{\mathbf{v}}\)`. If the point moves a distance of d units in the direction of
`\(\mathbf{v}\)`, the change in position is given by
`\(-d \hat{\mathbf{v}}\)`. This negative sign is crucial in indicating the direction of the change, ensuring that it aligns with the specified movement along
`\(\mathbf{v}\)`.

Understanding the directional components and sign conventions is essential in vector operations and applications, such as displacement calculations in physics or navigation. The negative sign, in this context, clarifies that the change in position is in the opposite direction to the vector
`\(\mathbf{v}\)`.