# If $\overrightarrow a=p\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow b=\sqrt q\hat i+5\hat k$ are two vectors of same magnitude, then no. of values of $(p,q)$ are?

$\begin{array}{1 1} (A) \text{Only one value} \\ (B) \text{two values of (p,q)} \\ (C) \text{Infinite values} \\ (D) \text{No value of (p,q)} \end{array}$

Since $|\overrightarrow a|=|\overrightarrow b|,\:\:p^2+9+16=q+25$
$\Rightarrow\:p^2=q$
$\therefore$ There are infinite real values of $(p,q)$ satisfying $p^2=q$