Equation of a line and a line segment Let ell be the line that passes through the points P0(−3, 5, 8) and P1(4, 2, −1). a. Find an equation of ell. b. Find parametric equations of the line segment that extends from P0 to P1.

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Equation of a line and a line segment Let ell be the line that passes through the points P0(−3, 5, 8) and P1(4, 2, −1).  a. Find an equation of ell.   b. Find parametric equations of the line segment that extends from P0 to P1.

Lynne Trussell · Accepted Answer

Step 1 Formula: The equation of line passing through the points A(x1, y1, z1) &amp;amp; B(x2, y2, z2) is given by: x−x1x2−x1=y−y1y2−y1=z−z1z2−z1 Step 2 The equation of line passing through the points P0=(−3, 5, 8)&amp;amp; P1=(4, 2, −1) is given by: x−(−3)4−(−3)=y−52−5=z−8−1−8 ⇒x+37=y−5−3=z−8−9 Hence, the equation of line is x+37=y−5−3=z−8−9 Step 3 The parametric equations of line segment is given by: x+37=y−5−3=z−8−9=t ⇒x+37=t, y−5−3=t, z−8−9=t ⇒x=7t−3, y=−3t+5, z=−9t+8 Hence, the parametric equations are: x=8t−3, y=−3t+5, z=−9t+8

Equation of a line and a line segment Let \ell

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