Question

Find the vector equation of the plane passing through the points i - 2j + 5k, -5j - k and -3i + 5j.

Answer 1

Answer:

Equation of the plane

3x-y-z=0

Step-by-step explanation:

To find the vector equation of the plane passing through the points i - 2j + 5k, -5j - k and -3i + 5j,

let A(1,-2,5)

B(0,-5,-1)

C(-3,5,0)

Equation of plane passing through three points

$\left|\begin{array}{ccc}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\end{array}\right|=0 \\\\so\\\\\\\left|\begin{array}{ccc}x-1&y+2&z-5\\0-1&-5+2&-1-5\\-3-1&5+2&0-5\end{array}\right| =0\\\\\\\left|\begin{array}{ccc}x-1&y+2&z-5\\-1&-3&-6\\-4&7&-5\end{array}\right| =0$

$=>(x-1)(15+42)-(y+2)(5-24)+(z-5)(-7-12)=0\\\\=>57x-57-19y-38-19z+95=0\\\\\\=> 57x-19y-19z=0\\\\=> 3x-y-z=0$

is the required equation of plane.

Answer 2

Step-by-step explanation:

Addition of vectors...