Represent the line segment from P to Q by a vector-valued function. (P corresponds to t=0. Q corresponds to t=1.) P(−4, −1, −1), Q(−1, −7, −3) r(t)=? Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)

Question

Represent the line segment from P to Q by a vector-valued function. (P corresponds to t=0. Q corresponds to t=1.)  P(−4, −1, −1), Q(−1, −7, −3)  r(t)=?  Represent the line segment from P to Q by a set of parametric equations. (Enter your answers as a comma-separated list of equations.)

kayleeveez7 · Accepted Answer

Step 1 Given, point P=(−4, −1, −1) and Q(−1, −7, −3) We know that line segment r(t) is given by r(t)=(1−t)r0+tr1, 0≤t≤1 Where r0=⟨−4, −1, −1⟩ and r1=⟨−1, −7, −3⟩ put this value in eq.(1) we get , r(t)=(1−t)⟨−4, −1, −1⟩+t⟨−1, −7, −3⟩ =⟨−4(1−t), −1(1−t), −1(1−t)⟩+⟨−1t, −7t, −3t⟩ =⟨−4+4t, −1+t, −1+⟨−t, −7t, −3t⟩ =⟨−4+4t−t, −1+t−7t, −1+t−3t⟩ =⟨−4+3t, −1−6t, −1−2t⟩ Hence the line segment is r(t)=⟨−4+3t, −1−6t, −1−2t⟩ this is the set of parametric equations r(t)=(−4+3t)i+(−1−6t)j+(−1−2t)k this is the vector valued function

Represent the line segment from P to Q by a vector-valued function. (P

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New Questions in Calculus 2