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A=[{:(l(1),m(1),n(1)),(l(2),m(2),n(2)),(...

`A=[{:(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2)),(l_(3),m_(3),n_(3)):}]` and `B=[{:(p_(1),q_(1),r_(1)),(p_(2),q_(2),r_(2)),(p_(3),q_(3),r_(3)):}]`
Where `p_(i), q_(i),r_(i)` are the co-factors of the elements `l_(i), m_(i), n_(i)` for `i=1,2,3`. If `(l_(1),m_(1),n_(1)),(l_(2),m_(2),n_(2))` and `(l_(3),m_(3),n_(3))` are the direction cosines of three mutually perpendicular lines then `(p_(1),q_(1), r_(1)),(p_(2),q_(2),r_(2))` and `(p_(3),q_(),r_(3))` are

A

the direction cosines of three mutually perpendicular lines

B

the direction ratios of three mutually perpendicular lines which are not direction cosines.

C

the direction cosines of three lines which need not be perpendicular

D

the direction of three lines which need not be perpendicular

Text Solution

Verified by Experts

The correct Answer is:
A
Let `veca=l_(1)hati+m_(1)hatj+n_(1)hatk, hatb=l_(2)hati+m_(2)hatj+n_(2)hatk` and `vecc=l_(3)hati+m_(3)hatj+n_(3)hatk`.
Given, that `veca, vecb,vecc` are three mutually perpendicular unit vectors.
Then `p_(1)hati+q_(1)hatj+r_(1)hatk=vecb xx vecc = veca`
`therefore vecb xx vecb` parallel to `veca` and `vecb xx vecc, veca` are unit vectors Similarly, `p_(2)hati+q_(2)hatj+r_(2)hatk=vecc xx veca = vecb`
and `p_(3)hati+q_(3)hatj+_(3)hatk=veca xx vecb = vecc`
These vectors are also mutually perpendicular unit vectors.
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