Mathematics: Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (5, 4, 0) and perpendicular to both i j and j k

here u goStep-by-step explanation:i got x=20...

Find parametric equations and symmetric equations

jaylynomalley

12.02.2022

Step-by-step explanation:

Suppose u = i + j = $\Big \langle 1,1,0 \Big\rangle$ & v = j + k = $\Big \langle 0,1,1 \Big\rangle$

The direction vector for the line u*v is:

$u\times v = \left |\begin{array}{ccc}i&j&k\\1&1&0\\0&1&1\end {array} \right|$

= (1-0) i - (1 - 0)j + ( 1- 0) k

= i - j - k

= $\Big \langle 1,-1,1 \Big\rangle$

Hence, the equation of the line via the point (5,4,0 ) and the direction vector $\Big \langle 1,-1,1 \Big\rangle$ is as follows:

r(t) = (5,4,0) + t $\Big \langle 1,-1,1 \Big\rangle$

r(t) = (5+t, 4-t, t)

The symmetric equations of the line are:

$\dfrac{x-5}{1}= \dfrac{y-4}{-1} = \dfrac{z}{1}$

x - 5 = -(y-4) = z

The parametric equation of the line is:

$\dfrac{x-5}{1}= \dfrac{y-4}{-1} = \dfrac{z}{1}= t$

x = 5 + t , y = 4 - t , z = t

0,0(0 оценок)