2.5 Applications of Products
Chapter
Chapter 2
Section
2.5
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Solutions 18 Videos

Find the projection of \vec{u} = (2, 3, -4) onto each of the coordinate axes.

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0.58mins
Q3

Find the projection of \vec{PQ} onto each of the coordinates axes, where P is the point (2,3, 5) and Q is the point (-1, 2, 5).

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0.57mins
Q4

a. Find the projection of an edge of a unit cube onto one of its body diagonals.

b. Find the projection of a boy diagonal of a unit cube onto one of its edges.

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Q5

Find the volume of a parallelepiped determined by the vectors \vec{a} = (2, -5, -1), \vec{b} = (4, 0, 1), and \vec{c} = (3, -1, -1).

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6.01mins
Q8

a 35-kg trunk is dragged 10 m up a ramp inclined at an angle of 12^o to the horizontal by a force of 90 N applied at an angle of 20^o to the ramp. At the top of the ramp, the trunk is dragged horizontally another 15 m by the same force. Find the total work done.

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Q14

Find the work done by a force \vec{F} that causes a displacement \vec{d}.

\vec{F} = 2\vec{i}, \vec{d} = 5\vec{i} +6\vec{j}

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0.27mins
Q15a

Find the work done by a force \vec{F} that causes a displacement \vec{d}.

\vec{F} = 4\vec{i}+\vec{j}, \vec{d} = 3\vec{i} + 10\vec{j}

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0.13mins
Q15b

Find the work done by a force \vec{F} that causes a displacement \vec{d}.

\vec{F} =(800, 600), \vec{d} = (20, 50)

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Q15c

Find the work done by a force \vec{F} that causes a displacement \vec{d}.

\vec{F} =12\vec{i}-5\vec{j}+ 5\vec{k}, \vec{d} =-2\vec{i} + 8\vec{j}- 4\vec{k}

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0.27mins
Q15d
Lectures 5 Videos

Torque Application of Cross Product

\vec{T} = \vec{F} \times \vec{r}

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Torque Application of Cross Product

Volume of Parallelpied

V = |(\vec{a} \times \vec{b})\cdot \vec{c} |

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4.12mins
Volume of Parallelpied

Projecting \vec{u} onto another \vec{v}.

Proj( \vec{u} on \vec{v}) = \displaystyle \frac{|\vec{u} \cdot \vec{v}|}{|\vec{v}|^2} \vec{v}

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Projection Vectors

Work = |\vec{F}||\vec{d}|\cos\theta

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Work Example