Respuesta :
Answer:
a) L(x,y,z) = (-4,0,2)+(2,8,-7)*t
b) (2-z)/7= y/8=(x+4)/2 (option B)
Step-by-step explanation:
the parametric equation of the line passing through the point P₀= (-4,0,2) and parallel to the vector v=2i + 8j - 7k is
L(x,y,z)=P₀+v*t
therefore
L(x,y,z) = (-4,0,2)+(2,8,-7)*t
or
x=x₀+vx*t = -4 + 2*t
y=y₀+vy*t = 8*t
z=z₀+vz*t = 2 -7*t
solving for t in the 3 equations we get the symmetric equation of the line:
(2-z)/7= y/8=(x+4)/2
thus the option B is correct
Answer:
a) Parametric equations
x = -4 + 2t
y = 8t
z = 2-7t
b) symmetric equations
[tex]\frac{x+4}{2}= \frac{y}{8} = \frac{z+2}{-7}[/tex] The answer is the option B
Step-by-step explanation:
For writing the vectorial equation of a line, we need a point in the line and its director vector, thus:
[tex]L: (x_{0},y_{0},z_{0} ) + t(a,b,c)[/tex]
Where [tex](x_{0},y_{0},z_{0})[/tex] is a point in the line
(a,b,c) is the director vector
Then
[tex]L: (-4,0,2) + t(2,8,-7)[/tex]
a) Parametric equations
Since the vectorial equation, we can obtain the parametric equations writing the equation for each component
x = -4 + 2t
y = 8t
z = 2-7t
b)Symmetric equations
Since the parametric equations, we isolate the parameter t
[tex]\frac{x+4}{2}= \frac{y}{8} = \frac{z+2}{-7}[/tex]
