. 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

a) Parametric equations

x = -4 + 2t

y = 8t

z = 2-7t

b) symmetric equations

         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:

                            Where   is a point in the line

                                           (a,b,c) is the director vector

Then

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

b.   e = 7.5h

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