A) \[\mu =\lambda +1\]
B) \[\lambda =\mu +1\]
C) \[\lambda +\mu =1\]
D) \[\mu =2+\lambda \]
Correct Answer: A
Solution :
We have,\[\overset{\to }{\mathop{\mathbf{P}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BD}}}\,=\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{BC}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,\] \[=\overset{\to }{\mathop{\mathbf{AC}}}\,+\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+(\overset{\to }{\mathop{\mathbf{AC}}}\,+\overset{\to }{\mathop{\mathbf{CD}}}\,)\] \[=\lambda \overset{\to }{\mathop{\mathbf{AD}}}\,+\overset{\to }{\mathop{\mathbf{AD}}}\,=(\lambda +1)\overset{\to }{\mathop{\mathbf{AD}}}\,\] But,\[\overset{\to }{\mathop{\mathbf{P}}}\,=\mu \overset{\to }{\mathop{\mathbf{AD}}}\,\] \[\therefore \] \[\mu =\lambda +1\]You need to login to perform this action.
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