
Review Question 4.1 When does a vector have a positive scalar component? When does a vector have a negative scalar component?

The condition under which a vector has a positive scalar component and a negative scalar component.
Answer to Problem 1RQ
Solution:
When the vector component is in the positive direction of the axis, the scalar component is positive.
When the vector component is in the negative direction of the axis, the scalar component is negative.
Explanation of Solution
Introduction:
The scalar component of vector is determined by the x-axis and the y-axis, which are perpendicular to each other. There is no need to use the vector component of
Explanation:
Consider the first case, when a vector is in the positive x-direction,
The following steps are used to draw the diagram,
(1) Draw an arrow that represents the vector
(2) Now, draw the x-axis and the y-axis, which are perpendicular to each other.
(3) Resolve the vector into components.
Here,
Resolve the magnitude of force
And,
Therefore, when the vector component is in the positive direction of the axis, the scalar component is positive.
Consider the second case, when a vector is in the negative x-direction,
Here,
Find the values of the scalar component as,
And,
Suppose
Here, the negative sign shows the direction of the vector.
Therefore, when the vector component is in the negative direction of the axis, the scalar component is negative.
Conclusion:
Thus, if the vector component is in the positive direction of the axis, then the scalar component is positive and, if the vector component is in the negative direction of the axis, the scalar component is negative.
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