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Question
If A=(3,1,2),B=(0,−1,−1),C=(−1,1,0) are three consecutive vertices of a parallelogram ABCD then the length of the diagonal BD is
If A=(3,1,2),B=(0,−1,−1),C=(−1,1,0) are three consecutive vertices of a parallelogram ABCD then the length of the diagonal BD is
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Solution
The correct option is D 6
We have →AB=−3^i−2^j−3^k
→BC=−1^i+2^j+^k
So line equation of Δ=(3,1,2)+t(−1,2,1)
→CD||→BA
(4−t)^i+2t^j+(2+t)^k=k(3^i+2^j+3^k)
t=k−1)
4−t=3t
t=1
So D=(2,3,3)
Length BD =√(2)2+(4)2+42
=6
We have
→AB=−3^i−2^j−3^k
→BC=−1^i+2^j+^k
→BC=−1^i+2^j+^k
So line equation of Δ=(3,1,2)+t(−1,2,1)
→CD||→BA
(4−t)^i+2t^j+(2+t)^k=k(3^i+2^j+3^k)
t=k−1)
4−t=3t
t=1
t=k−1)
4−t=3t
t=1
So D=(2,3,3)
Length BD =√(2)2+(4)2+42
=6
=6
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