Find a parametrization for the line segment joining the points.
-(2, -7, -2), (0, -7, 4)
A) $x = 2 t , y = - 7 t , z = - 6 t + 4,0 \leq t \leq 1$
B) $x = - 2 t + 2 , y = - 7 t , z = 6 t - 2,0 \leq t \leq 1$
C) $x = - 2 t + 2 , y = - 7 , z = 6 t - 2,0 \leq t \leq 1$
D) $x = 2 t , y = - 7 , z = - 6 t + 4,0 \leq t \leq 1$

Question

Find a parametrization for the line segment joining the points.
-(2, -7, -2), (0, -7, 4) 
A) $x = 2 t , y = - 7 t , z = - 6 t + 4,0 \leq t \leq 1$
B) $x = - 2 t + 2 , y = - 7 t , z = 6 t - 2,0 \leq t \leq 1$
C) $x = - 2 t + 2 , y = - 7 , z = 6 t - 2,0 \leq t \leq 1$
D) $x = 2 t , y = - 7 , z = - 6 t + 4,0 \leq t \leq 1$

Quizplus · Accepted Answer

A parametrization of a line segment from point $A(x_1, y_1, z_1)$ to point $B(x_2, y_2, z_2)$ can be given by $x = x_1 + (x_2 - x_1)t$, $y = y_1 + (y_2 - y_1)t$, $z = z_1 + (z_2 - z_1)t$, where $0 \leq t \leq 1$. For the points (2, -7, -2) and (0, -7, 4), this gives $x = 2 + (0 - 2)t = 2 - 2t$, $y = -7 + (-7 + 7)t = -7$, $z = -2 + (4 + 2)t = -2 + 6t$, which matches option C.

Find a Parametrization for the Line Segment Joining the Points x=2t,y=−7t,z=−6t+4,0≤t≤1x = 2 t , y = - 7 t , z = - 6 t + 4,0 \leq t \leq 1x=2t,y=−7t,z=−6t+4,0≤t≤1

Find a Parametrization for the Line Segment Joining the Points $x = 2 t , y = - 7 t , z = - 6 t + 4,0 \leq t \leq 1$