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Question

If the coordinate of points P(2,3,4),Q(1,-2,1), and O is the origin then:


A

OP=OQ

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B

OPOQ

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C

OPOQ

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D

None of these

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Solution

The correct option is B

OPOQ


Explanation for the correct option.

Step 1: Find the direction ratios

The direction cosines of the coordinate a,b,c is aa2+b2+c2,ba2+b2+c2,ca2+b2+c2

The direction ratio of line segment OP are given by

229,329,429
So,l1=229,m1=329,n1=429

Step 2: Find the direction ratios

Direction ratios of the line segment OQ are given by:
16,-26,16
So, I2=16,m2=-26,n2=16

Step 3: Determine perpendicularity

We know for perpendicular lines, l1l2+m1m2+n1n2=0.
l1l2+m1m2+n1n2=229×16+329×-26+429×16=2174-6174+4174=0

Hence, option B is correct.


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