Find the vector and parametric equations for the line segment connecting P to Q.P(0, - 1, 1), Q(1/2, 1/3, 1/4)

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Szeteib · Accepted Answer

Vector equation of a line segment joining the points with position vectors r0 and r1 is  r=(1−t)r0+tr1  Where t∈[0,1]  Substitute r0=&amp;lt;0,−1,1&amp;gt; and r1=&amp;lt;12.13,14&amp;gt;  r(t)=(1−t)(0,−1,1)+t&amp;lt;12,13,14&amp;gt;  r(t)=&amp;lt;0,−1+t,1−t&amp;gt;+&amp;lt;t2,t3,t4&amp;gt;  r(t)=&amp;lt;t2,−1+4t3,1−3t4&amp;gt;  Where t∈[0,1] The parametric equations for the line segment are  x=t2,y=−1+4t3,z=1−3t4  Where t∈[0,1]

madeleinejames20 · Accepted Answer

Answer:x=t2y=−1+t3z=1+t4Explanation:To find the vector and parametric equations for the line segment connecting points P and Q, we can use the following steps:1. Find the direction vector:v→=PQ→=Q→−P→2. Calculate the parametric equations:x=xP+tvxy=yP+tvyz=zP+tvzNow, let&#039;s calculate the values using the given points P(0, -1, 1) and Q(1/2, 1/3, 1/4):1. Direction vector:v→=Q→−P→=(12,13,14)−(0,−1,1)2. Parametric equations:x=0+t(12)y=−1+t(13)z=1+t(14)

Eliza Beth13 · Accepted Answer

Step 1. Calculate the vector 𝐯 that represents the direction of the line segment. This can be done by subtracting the coordinates of point P from the coordinates of point Q:𝐯=𝐐−𝐏=(121314)−(0−11)=(1213+114−1)=(1243−34).Step 2. Express the parametric equations for the line segment using the vector 𝐯 and the coordinates of point P. Let&#039;s denote the parameter as t:𝐫(t)=𝐏+t𝐯=(0−11)+t(1243−34).The parametric equations can also be written component-wise as:x(t)=0+12t,y(t)=−1+43t,z(t)=1−34t.These equations describe the line segment connecting points P and Q.

Mr Solver · Accepted Answer

To find the vector and parametric equations for the line segment connecting points P and Q, we can use the following steps:1. Find the vector PQ→, which represents the displacement from point P to point Q:PQ→=[Qx−PxQy−PyQz−Pz]Substituting the coordinates of P and Q:PQ→=[12−013−(−1)14−1]Simplifying:PQ→=[1243−34]2. The parametric equations for the line segment can be written as follows:x=Px+t·PQ→xy=Py+t·PQ→yz=Pz+t·PQ→zSubstituting the coordinates of point P and the components of PQ→:x=0+t·12y=−1+t·43z=1+t·(−34)Simplifying, we get the parametric equations for the line segment:x=t2y=−1+4t3z=1−3t4These equations describe the line segment connecting points P(0, -1, 1) and Q(12, 13, 14).

Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4)

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