. 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. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

x = 23.78

step-by-step explanation: