Question

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

Answer 1

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>

`A* B=\begin{vmatrix}i&j&k\\1&1&0\\0&1&1\end{vmatrix}`

`A* B=i-j+k`

Let v
`=A* B=i-j+k`

`v=<a,b,c>=<1,-1,1>`

`r_0=<x_0,y_0,z_0>=<3,1,0>`

`r=r_0+vt`

Substitute the values then we get

`r=<3,1,0>+t<1,-1,1>`

`r=<3+t,1-t,t>`

The parametric equation of the line

`x=x_0+at,y=y_0+bt,z=z_0+ct`

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

`x=3+t,y=1-t,z=t`

The symmetric equation of the line is given by

`(x-x_0)/(a)=(y-y_0)/(b)=(z-z_0)/(c)`

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

`(x-3)/(1)=(y-1)/(-1)=z`