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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pramodpandey | College Teacher | (Level 3) Valedictorian

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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


let x=k  some real nos.


substituting these value in (i) ,we have


Thus pont of intersection of these three planes are

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


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