Question

Find the vector equation of the plane passing through the points (0, 0, 0), (0, 5, 0) and (2, 0, 1).

Answer 1

Answer:

Vector equation of plane

$\vec r.(-\hat i+2\hat k)=0$

Step-by-step explanation:

To find the vector equation of the plane passing through the points (0, 0, 0), (0, 5, 0) and (2, 0, 1).

I am going to solve this by cartesian form if three points are (x1,y1,z1) (x2,y2,z2)

(x3,y3,z3)

$\left|\begin{array}{ccc}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\end{array}\right|=0 \\\\so\:\:here\:\:\\A(0,0,0)\:\:B(0,5,0)\:\:C(2,0,1)\\\\\\\left|\begin{array}{ccc}x-0&y-0&z-0\\0-0&0-5&0-0\\2-0&0-0&1-0\end{array}\right| =0\\\\\\\left|\begin{array}{ccc}x&y&z\\0&-5&0\\2&0&1\end{array}\right| =0\\\\\\=> -5x+10z=0\\\\or\\\\\\=> -x+2z=0$

This is the equation of plane in cartesian form.

So in vector form

$\vec r.(-\hat i+2\hat k)=0$

Answer 2

Step-by-step explanation:

This Is the answer for the above problem