A) -6
B) -4
C) 6
D) 4
Correct Answer: A
Solution :
Now,\[\overrightarrow{\mathbf{AB}}+2\overrightarrow{\mathbf{AD}}+\overrightarrow{\mathbf{BC}}-2\overrightarrow{\mathbf{DC}}\] \[=\overrightarrow{\mathbf{AC}}+2\overrightarrow{\mathbf{AD}}-2\overrightarrow{\mathbf{DC}}\] \[=\overrightarrow{\mathbf{AC}}+2(\overrightarrow{\mathbf{AC}}+\overrightarrow{\mathbf{CD}})-2\overrightarrow{\mathbf{DC}}\] \[=3\overrightarrow{\mathbf{AC}}-4\overrightarrow{\mathbf{DC}}\] \[=3(2\overrightarrow{\mathbf{QC}})-4\left( \frac{3}{2}\overrightarrow{\mathbf{PC}} \right)\] \[=6\overrightarrow{\mathbf{QC}}-6\overrightarrow{\mathbf{PC}}=6(\overrightarrow{\mathbf{QC}}+\overrightarrow{\mathbf{CP}})\] \[\Rightarrow \] \[k\overrightarrow{\mathbf{PQ}}=6\overrightarrow{\mathbf{QP}}=6\overrightarrow{\mathbf{PQ}}\] (given) \[\Rightarrow \] \[k=-6\]You need to login to perform this action.
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