# Consider the three planes x+ y -z = 0 3x -3y + z = 0 4x + y -2z = 0 Find the intersection of these three planes.

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### 1 Answer

Equation of planes a

X+y-z=0 (i)

3x-3y+z=0 (ii)

4x+y-2z=0 (iii)

Three planes intersect at a point provided they are not parallel.

adding (i) to (ii)

4x-2y=0 (iv)

adding -2 times(i) to (iii) ,we have

2x-y=0 (v)

(iv) is multiple of (v) ,so we have

2x=y

let x=k some real nos.

y=2k

substituting these value in (i) ,we have

z=3k

Thus pont of intersection of these three planes are

(k,2k,3k) , k is real numbers.