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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra

If $\overrightarrow a=\hat i+\hat j-\hat k,\:\overrightarrow b=-\hat i+2\hat j+\hat k\:\:and\:\:\overrightarrow c=-\hat i+2\hat j-\hat k$, then a unit vector $\perp$ to $\overrightarrow a+\overrightarrow b$ and $\overrightarrow b+\overrightarrow c$ is ?

$\begin{array}{1 1} (A) \hat i \\ (B) \hat j \\ (C) \hat k \\ (D) \large\frac{1}{\sqrt 3}(\hat i+\hat j+\hat k) \end{array} $

1 Answer

$\overrightarrow a+\overrightarrow b=3\hat j$ and $\overrightarrow b+\overrightarrow c=-2\hat i+4\hat j$
A vector along the direction $\perp$ to $\overrightarrow a+\overrightarrow b\:\:and\:\:\overrightarrow b+\overrightarrow c$ is
$(\overrightarrow a+\overrightarrow b)\times(\overrightarrow b+\overrightarrow c)=\left|\begin{array}{ccc}\hat i & \hat j & \hat k\\0 &3 &0\\-2 & 4 & 0\end {array}\right|$ $=6\hat k$
$\therefore$ Unit vector in this direction is $\hat k$
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