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If the points 2a+3b-c, a-2b+3c, 3a+lambd...

If the points `2a+3b-c, a-2b+3c, 3a+lambda b-2c` and `a-6b+6c` are coplanar, then the direction cosines of the vector `lambda hat(i)-2lambda hat(j)+hat(k)` are

A

`(2)/(sqrt(21)), (-4)/(sqrt(21)), (1)/(sqrt(21))`

B

`- (2)/(sqrt(78)), (5)/(sqrt(78)), (7)/(sqrt(78))`

C

`4/9, 8/9, 1/9`

D

`2/3, - 2/3, - 1/3`

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The correct Answer is:
C
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