Mathematics: . Find sets of parametric equations and symmetric equations of the line through the point parallel to the given vector or line (if possible). Point (-4,0,2) Parallel to v=2i + 8j - 7k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations A. 2x= y/8 = 7z B. (x+4)/2 = y/8 = (2-z)/7 C x/2 = y = z/7 D. (x-4)/2 = y = z/7

my manStep-by-step explanation:...

. Find sets of parametric equations and symmetric

madisonworthington7

20.01.2022

a) Parametric equations

x = -4 + 2t

y = 8t

z = 2-7t

b) symmetric equations

$\frac{x+4}{2}= \frac{y}{8} = \frac{z+2}{-7}$ 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:

$L: (x_{0},y_{0},z_{0} ) + t(a,b,c)$

Where $(x_{0},y_{0},z_{0})$ is a point in the line

(a,b,c) is the director vector

Then

L: (-4,0,2) + t(2,8,-7)

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

$\frac{x+4}{2}= \frac{y}{8} = \frac{z+2}{-7}$

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