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>

$A\times B=\begin{vmatrix}i&j&k\\1&1&0\\0&1&1\end{vmatrix}$

$A\times B=i-j+k$

Let v$=A\times B=i-j+k$

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

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

$r=r_0+vt$

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

$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$

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

$\frac{x-3}{1}=\frac{y-1}{-1}=z$