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Question

If O is the origin and OP=3 with direction ratios -1,2,-2, then co-ordinates of P are


A

1,2,2

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B

-1,2,-2

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C

-3,6,9

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D

-13,23,-23

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Solution

The correct option is B

-1,2,-2


Explanation for the correct option:

Step 1 : given information

Here, the distance between the origin and point P will be denoted by d which is equal to 3.

Now, suppose the coordinates of the point P are ld,md,nd, where l,m,n are the cosine ratios.

Denote the direction ratio -1,2,-2 as a,b,c. Then the cosine ratios are given by,

l=aa2+b2+c2,m=ba2+b2+c2,andn=ca2+b2+c2

Step 2 : finding the coordinates of the point P

The cosine ratios will be,

l=-1-12+22+-22=-11+4+4=-19=-13

Similarly, mandn will be 23and-23

Since, the coordinates of the point P are ld,md,nd, then

P=-133,233,-233=-1,2,-2

Hence, the correct option is (B).


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