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Lines OA, OB are drown from O with direc...

Lines `OA, OB` are drown from `O` with direction cosines proportional to `(1,-2, -1) ; (3 -2,3).` Find the direction cosines of the normal to the plane `AOB.`

A

`(4,3,2)`

B

`(4,-3,-2)`

C

`(-4,3,-2)`

D

`(4,3,-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let a parallel to line Oa is `hati-2hatj-hatk`
b parallel to line OB is `3hati-2hatj+3hatk`
Now , `axxb=|{:(hati" "hatj" "hatk),(1" "-2" "-1),(3" "-2" "3):}|=8hati-6hatj+4hatk`
`therefore`Required DR's are -8,-6,4 or 4,3,-2
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