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

Question

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 

Answer 1

Step 1:

(a)

The parallel vector is .

The direction vector is .

The point is .

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

and .

Substitute and in parametric equations.

Parametric equations are and .

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 and in symmetric equations.

.

The symmetric equations are .

Solution:

(a) Parametric equations are and .

(b) Symmetric equations are .

Direction numbers as integers: and .