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