How do you find parametric equations and symmetric equations for the line through #(3, −2, 5)# and parallel to the line #x + 3 = y/2 = z − 2#?

Answer 1

The symmetric form is:

#(x-x_0)/a=(y-y_0)/b=(z-z_0)/c#

The parametric forms are:

#x=at+x_0,y=bt+y_0, and z = ct+z_0#

Given: #x + 3 = y/2 = z − 2#

Rewrite in symmetric form:

#(x - (-3))/1 = (y- 0)/2 = (z − 2)/1#
Please observe that the current point is #(-3,0,2)#
Change to the #(3, -2, 5)#
#(x - 2)/1 = (y- (-2))/2 = (z − 5)/1#
Please observe that #a = 1, b = 2, and c = 1#; this gives us the parametric forms:
#x = t+ 3, y = 2t-2, and z = t+5#
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Answer 2

Parametric equations for the line are:

x = 3 + t y = -2 + 2t z = 5 + t

Symmetric equations for the line are:

(x - 3) / 1 = (y + 2) / 2 = (z - 5) / 1

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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