Represent the line segment from P(-2, -3, 8), Q(5, 1, -2) by a vector-valued function and by a set of parametric equations.

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Wriedge · Accepted Answer

We have, points P(-2, -3, 8) and Q(S, 1, -2) Now, the component vector from P to Q, v(t)=&amp;lt;5−(−2),1−(−3),−2−8&amp;gt; ⇒v(t)=&amp;lt;7,4,−10&amp;gt; So, the direction number are a = 7,6 = 4 and c= -10 For initial point on the line, use point P(-2,-3.8) We get, xcirc=−2,ycirc=−3 and zcirc=8 Now, to form the parametric equation : x=x∘+at,y=y∘+btandz=z∘+ct…….(1) Putting the value of a=7,b =4, c= -10 and x∘=−2,y∘=−3z∘=8 in eq. (1), we get x=−2+7t,y=−3+4tandz=8−10t Now, to forma vector - valued function : r(t)=x(t)i+y(t)j+z(t)k We have, x=−2+7t,y=−3+4tandz=8−10t So, r(t)=(7t−2)i+(4t−3)j+(8−10t)k Hence, set of parametric equations be,x=−2+7t,y=−3+4tandz=8−10t and vector - valued function be, r(t)=(7t−2)i+(4t−3)j+(8−10t)k

Represent the line segment from P(-2, -3, 8), Q(5, 1,

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