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In a trapezium ABCD the vector B vec C ...

In a trapezium ABCD the vector `B vec C = lambda vec(AD).` If `vec p = A vec C + vec(BD)` is coillinear with `vec(AD)` such that `vec p = mu vec (AD),` then

A

`mu=lamda+1`

B

`lamda=mu+1`

C

`lamda+mu=1`

D

`mu=2+lamda`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `p=AC+BD=AC+BC+CD`
`=AC+lamdaAD+CD`
`=lamdaAD+(AC+CD)=lamdaAD+AD=(lamda+1)AD`
Therefore, `p=muAD impliesmu=lamda+1`.
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