A) exactly one value of (p, q)
B) exactly two values of (p, q)
C) more than two but not all values of (p, q)
D) all values of (p, q)
Correct Answer: A
Solution :
\[3{{p}^{2}}[\overrightarrow{u}\overrightarrow{v}\overrightarrow{w}]-pq[\overrightarrow{u}\overrightarrow{v}\overrightarrow{w}]+2{{q}^{2}}[\overrightarrow{u}\overrightarrow{v}\overrightarrow{w}]=0\] \[\Rightarrow \]\[3{{p}^{2}}pq+2{{q}^{2}}=0\] \[p=\frac{q\pm \sqrt{1-24}q}{2\times 3}\] \[p=\frac{q\pm \sqrt{23}iq}{2\times 3}\]\[\Rightarrow \] \[p=0,\text{ }q=0\]
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