Find sets of parametric equatons and symmetric equations of the

pamangking8

pamangking8

Answered question

2021-11-30

Find sets of parametric equatons and symmetric equations of the line tha passes though the given point and is parallel to the given vector or line
PointParallel to(1, 0, 8)v=3i+4j8k
a) parametric equations
b) symmetric equations
x+13=y4=8z8

Answer & Explanation

Momp1989

Momp1989

Beginner2021-12-01Added 21 answers

Step 1
Given:
The given point is (1, 0, 8) and the vector or line is v=3i+4j8k
To determine: The 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.
Step 2
a) The parametric equations for a line passing through (x0, y0, z0) and parallel to the vector v=ai+bj+ck are
x=x0+at, y=y0+bt, z=z0+ct
The required parametric equations are
x=1+3t, y=4t, z=88t
Step 3
b) The parametric equations are
x=1+3t, y=4t, z=88t
Solving for t we have,
t=x+13, t=y4, t=z88
x+13=y4=z88
x+13=y4=8z8
Symmetric equations
x+13=y4=8z8

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