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If P(0,1,2),Q(4,-2,1) and O(0,0,0) are t...

If `P(0,1,2),Q(4,-2,1)` and `O(0,0,0)` are three points, then `/_POQ=`

A

`pi/6`

B

`pi/4`

C

`pi/3`

D

`pi/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Direction ratios of OP and OQ are (0,1,2) and (4,-2,1) respectvely
`costheta=(a_1a_2+b_1b_2+c_1c_2)/(sqrt(a_1^2+b_1^2+c_1^2)sqrt(a_2^2+b_2^2+c_2^2))`
`rArrcostheta=(0-2xx1+2xx1)/(sqrt(0+1+4)sqrt(16+4+1))=0`
`rArr" "theta=pi/2" "[thereforecos""pi/2=0]`
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