Chapter 9: Problem 39
State the definition of a cylinder.
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In Exercises 75 and \(76,\) sketch the vector \(v\) and write its component form. \(\mathbf{v}\) lies in the \(y z\) -plane, has magnitude 2 , and makes an angle of \(30^{\circ}\) with the positive \(y\) -axis.
Write an equation whose graph consists of the set of points \(P(x, y, z)\) that are twice as far from \(A(0,-1,1)\) as from \(B(1,2,0)\)
Find \((\mathbf{a}) \mathbf{u} \cdot \mathbf{v},(\mathbf{b}) \mathbf{u} \cdot \mathbf{u},(\mathbf{c})\|\mathbf{u}\|^{2},(\mathbf{d})(\mathbf{u} \cdot \mathbf{v}) \mathbf{v}\) and \((e) u \cdot(2 v)\). $$ \mathbf{u}=\mathbf{i}, \quad \mathbf{v}=\mathbf{i} $$
A toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a \(20^{\circ}\) angle with the horizontal. Find the work done in pulling the wagon 50 feet.
An object is pulled 10 feet across a floor, using a force of 85 pounds. The direction of the force is \(60^{\circ}\) above the horizontal. Find the work done.
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