Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point Parallel to (−3, 0, 3) v = 8i + 4j − 6k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations x/8=y=z/6 (x+3)/8=y/4=(3-z)/6 8x=y/4=6z (x-3)/8=y=z/6

Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.) Point Parallel to (−3, 0, 3) v = 8i + 4j − 6k (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations x/8=y=z/6 (x+3)/8=y/4=(3-z)/6 8x=y/4=6z (x-3)/8=y=z/6

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.6: Equations Of Lines And Planes

Problem 37E

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Point		Parallel to
(−3, 0, 3)		v = 8i + 4j − 6k

(a) parametric equations (Enter your answers as a comma-separated list.)

(b) symmetric equations

x/8=y=z/6

(x+3)/8=y/4=(3-z)/6

8x=y/4=6z

(x-3)/8=y=z/6

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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