Chapter 9: Problem 105
Find an equation of the plane with \(x\) -intercept \((a, 0,0),\) \(y\) -intercept \((0, b, 0),\) and \(z\) -intercept \((0,0, c) .\) (Assume \(a\) \(b,\) and \(c\) are nonzero. \()\)
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Find the component form and magnitude of the vector \(u\) with the given initial and terminal points. Then find a unit vector in the direction of \(\mathbf{u}\). \(\frac{\text { Initial Point }}{(4,-5,2)}\) \(\frac{\text { Terminal Point }}{(-1,7,-3)}\)
The vector \(\mathbf{u}=\langle 3240,1450,2235\rangle\) gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector \(\mathbf{v}=\langle 1.35,2.65,1.85\rangle\) gives the prices (in dollars) per unit for the three food items. Find the dot product \(\mathbf{u} \cdot \mathbf{v},\) and explain what information it gives.
Find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(2 \mathbf{z}-3 \mathbf{u}=\mathbf{w}\)
Find the vector \(z,\) given that \(\mathbf{u}=\langle 1,2,3\rangle\) \(\mathbf{v}=\langle 2,2,-1\rangle,\) and \(\mathbf{w}=\langle 4,0,-4\rangle\) \(\mathbf{z}=5 \mathbf{u}-3 \mathbf{v}-\frac{1}{2} \mathbf{w}\)
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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