A) 1
B) -2
C) 4
D) -4
Correct Answer: D
Solution :
Let \[\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k},\overrightarrow{b}=\hat{i}+2\hat{j}-3\hat{k}\]and \[\overrightarrow{c}=3\hat{i}+p\hat{j}+5\hat{k}\] Since,\[\overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c}\]are coplanar. \[\therefore \] \[[\overrightarrow{a}\text{ }\overrightarrow{b}\text{ }\overrightarrow{c}]=0\] \[\Rightarrow \] \[\left| \begin{matrix} 2 & -1 & 1 \\ 1 & 2 & -3 \\ 3 & p & 5 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[2(10+3p)+1(5+9)+1(p-6)=0\] \[\Rightarrow \] \[20+6p+14+p-6=0\] \[\Rightarrow \] \[7p+28=0\] \[\Rightarrow \] \[p=-\frac{28}{7}=-4\]
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