Question

A rope connecting points A and B supports the force F shown in the figure. Write expressions using Cartesian vector representation for the following: (a) \vec{r}_{AB}: the position vector from A to B. (b) \vec{r}_{BA}: the position vector from B to A. (c) \hat{u}_{AB}: the unit vector in the direction from A to B. (d) \hat{u}_{BA}: the unit vector in the direction from B to A. (e) \vec{F}_{AB}: the force vector the rope applies to A. (f) \vec{F}_{BA}: the force vector the rope applies to B.

          A rope connecting points A and B supports the force F shown in the figure.
Write expressions using Cartesian vector representation for the following:
(a) \vec{r}_{AB}: the position vector from A to B.
(b) \vec{r}_{BA}: the position vector from B to A.
(c) \hat{u}_{AB}: the unit vector in the direction from A to B.
(d) \hat{u}_{BA}: the unit vector in the direction from B to A.
(e) \vec{F}_{AB}: the force vector the rope applies to A.
(f) \vec{F}_{BA}: the force vector the rope applies to B.

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A rope connecting points A and B supports the force F shown in the figure.
Write expressions using Cartesian vector representation for the following:
(a) r⃗AB: the position vector from A to B.
(b) r⃗BA: the position vector from B to A.
(c) ûAB: the unit vector in the direction from A to B.
(d) ûBA: the unit vector in the direction from B to A.
(e) F⃗AB: the force vector the rope applies to A.
(f) F⃗BA: the force vector the rope applies to B.

Added by Kim S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Justin Swantek

Step 1

This is a vector that starts at A and ends at B. In Cartesian coordinates, we can represent this as r_AB = 4i + 3j (where i and j are the unit vectors in the x and y directions, respectively). Show more…

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Please help A rope connecting points A and B supports the force F shown in the figure Write expressions using Cartesian vector representation for the following: 4 m (a) r AB: the position vector from A to B. A F=12kN 3 m (b) r BA: the position vector from B to A. (c) uAB: the unit vector in the direction from A to B. B (d) uA: the unit vector in the direction from B to A. (e) FAb: the force vector the rope applies to A. (f)FpA: the force vector the rope applies to B.

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