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Let x, y, z are distinct cube roots of u...

Let x, y, z are distinct cube roots of unity and the value of `|[x,y-z,z-y],[x-z,y,z-x],[x-y,y-x,z]|=K` then `|K|`

A

(3,4,5)

B

(4,6,7)

C

(4,5,8)

D

(8,4,5)

Text Solution

Verified by Experts

The coordinates of any point of the given line are given by
`(x-3)/1=(y-4)/2=(z-5)/2=lamda`
Suppose the given line cuts the given plane at `(lamda+3,2lamda+4,2lamda+5)`
This lies on the plane.
`:.lamda+3+2lamda+4+2lamda+5=17implieslamda=1`
Hence the coordinates of the required point are (4,6,7).
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