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Q.

For a non-zero real number x.If the points with position vevectors (x-u) i+xj+xk, xi+(x-v) j+xk+xj+(x-w)k  and (x-1)i+(x-1)j+(x-1)k are coplanar, then

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a

u + v + w = 1

b

uvw = 1

c

1u+1v+1w=1

d

uv + vw + uw = 1

answer is C.

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Detailed Solution

AB=ui-vj AC=ui-wk AD=(u-1)i-j-k u-v0u0-wu-1-1-1=0  u(0-w)+v(-u+w(u-1))=0 -uw-vu+vuw-vw=0 vuw=uv+vw+wu

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