Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (3, 1, 0) and perpendicular to both i + j and j + k

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Answer with Step-by-step explanation:

We are given that a point (3,1,0)

Two vectors are

A=<1,1,0>

B=<0,1,1>

[tex]A\times B=\begin{vmatrix}i&j&k\\1&1&0\\0&1&1\end{vmatrix}[/tex]

[tex]A\times B=i-j+k[/tex]

Let v[tex]=A\times B=i-j+k[/tex]

[tex]v=<a,b,c>=<1,-1,1>[/tex]

[tex]r_0=<x_0,y_0,z_0>=<3,1,0>[/tex]

[tex]r=r_0+vt[/tex]

Substitute the values then we get

[tex]r=<3,1,0>+t<1,-1,1>[/tex]

[tex]r=<3+t,1-t,t>[/tex]

The parametric equation of the line

[tex]x=x_0+at,y=y_0+bt,z=z_0+ct[/tex]

Using the formula

The parametric equation of the line which is passing through the point (3,1,0) and perpendicular to both i+j and j+k is given by

[tex]x=3+t,y=1-t,z=t[/tex]

The symmetric equation of the line is given by

[tex]\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}[/tex]

Using the formula

The symmetric equation of the line which is passing through the point (3,1,0) and perpendicular to both i+j and j+k is given by

[tex]\frac{x-3}{1}=\frac{y-1}{-1}=z[/tex]

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