Step by step solution to "Find parametric equations for the lines in The..."

College
Calculus and Analysis
Integral Calculus
Parametric equations, polar coordinates, and vector-valued functions

Josalynn

Answered question

2021-02-12

Find parametric equations for the lines in The line through the origin parallel to the vector

2 j + k

Answer & Explanation

Arham Warner

Skilled2021-02-13Added 102 answers

Step 1 Given The vector equation is $0 i + 2 j + k$ The line passing through origin , origin is ( 0 ,0 ,0) The parametric equations for the line passing through the point $p 0 = (x_{0}, y_{0}, z_{0})$ and parallel to the vector is $v = (a i + b j + c k)$
$x = x_{0} + a t, y = y_{0} + b t, z = z_{0} + c t$

Step 2 To find parametric equations for the lines Here $a = 0, b = 2, c = 1, x_{0} = 0, y_{0} = 0 a n d z_{0} = 0$

Now plug this values in parametric equation $x = 0 + 0 t, y = 0 + 2 t, z = 0 + 1 t$
$x = 0, y = 2 t, z = t$

Therefore parametric equations for the line is $x = 0, y = 2 t a n d z = t$ .

2022-06-19

Po=(0,0,0) V=0i+2j+2

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