Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations P(0, 0, 0), Q(5, 2, 2)

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Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations  P(0, 0, 0), Q(5, 2, 2)

Alfonso Miller · Accepted Answer

Step 1 Given information: The point are P(0, 0, 0), Q(5, 2, 2) Calculation: Find the vector valued function. v(t)=⟨(5−0), (2−0), (2−0)⟩ ⟨3, 2, 2⟩ The direction numbers are ⟨5, 2, 2⟩ a=5, b=2, c=2 The value of (0, 0, 0) that is the initial points on the line x0=0, y0=0, z0=0 Step 2 The form of the parametric equations x=x0+at, y=y0+bt, z=z0+ct Substitute x0=0, y0=0, z0=0, a=5, b=2, c=2 in the parametric equations x=0+5t y=0+2t z=0+2t We get x=5t y=2t z=2t Step 3 Find the vector valued function r(t)=x(t)i+y(t)j+z(t)k =(5t)i+(2t)j+(2t)k Answer: r(t)=(5t)i+(2t)k

Represent the line segment from P to Q by a

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