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Symmetric equations of the line through the point parallel to the given vector or line (if possible).

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Find sets of (a) parametric equations and (b) Symmetric equations of the line through the point parallel to the given vector or line (if possible). (For each line, write the direction numbers as integers.)

Point                                                   parallel to

(- 2, 0, 3)                                             V = 2i + 4j - 2k 

asked Feb 18, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

(a)

The parallel vector is .

The direction vector is image.

The point is .

The parametric equations passing through the point and parallel to the direction vector are

and .

Substitute image and image in parametric equations.

Parametric equations are image and image.

Step 2:

(b)

Symmetric equations:

If the direction numbers and are all non zero, then eliminate the parameter to obtain symmetric equations of the line.

.

Substitute image and image in symmetric equations.

image.

The symmetric equations are image.

Solution:

(a) Parametric equations are image and image.

(b) Symmetric equations are image.

Direction numbers as integers: image and image.

answered Feb 23, 2015 by Sammi Mentor

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