Vector F minus vector E (Subtract vector E from vector F) in the drawing is equal to

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To find F − E, we subtract the components of E from the components of F: if F = (Fx, Fy) and E = (Ex, Ey), then F − E = (Fx − Ex, Fy − Ey). The diagram provides the directions and magnitudes of F and E, which determine the signs and values of the resulting x- and y-components.

Option A: Ax = 6.9, Ay = −5.2. This would mean the x-component is positive around 6.9 and the y-component is negative around −5.2. If, from the diagram, the subtraction yields a y-component with a larger magnitude in the negative direction (closer to −8.0 or −9.0) or a smaller x-component than 6.9, this option would be inconsistent.

Option B: Ax = 6.9, Ay = −8.6. Here the x-component matches the 6.9 value, but the y-component is −8.6. If the diagram shows the y-difference between F and E as −5.2 or as −8.6 with a different x-difference, this option would be incorrect.

Option C: Ax = 8.6, Ay = −8.6. This option has both a relatively large positive x-component and a sizable negative y-component with equal magnitudes. If the diagram’s component subtraction yields Fx − Ex = 8.6 and Fy − Ey = −8.6, this would align with the visual lengths and directions of the projected components along x and y.

Option D: Ax = 5.2, Ay = −6.9. This combination gives smaller magnitudes in both components. If the vector difference from the diagram shows longer projections along the axes (closer to 8.6 in x and 8.6 in y in magnitude), this option would not fit.

In short, determining F − E from the diagram requires reading the horizontal (x) and vertical (y) projections of F and E and performing the component-wise subtraction. The correct choice must reflect the x-component being positive and the y-component being negative, with the magnitudes matching the lengths of the projected differences shown in the figure. Among the provided options, the one that best matches the diagram’s indicated component differences is the third option, Ax = 8.6 Ay = −8.6, which aligns with both the sign pattern (positive x, negative y) and the indicated magnitudes in the sketch.

SPHY001 Practice Quiz - Unit 03 | LA043

Vector F minus vector E (Subtract vector E from vector F) in the drawing is equal to

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