The vector $\vec r$ satisfying the conditions that
(i) it is perpendicular to $3\hat i+2\hat j+2\hat k$ and $18\hat i -22\hat j-5\hat k$
(ii) it makes an obtuse angle with y-axis,
(iii) $|\vec r|=14$, is
Answer & explanation
Correct answer: option 1
Let $\vec a = 3\hat i+2\hat j+2\hat k$ and $\vec b = 18\hat i -22\hat j-5\hat k$
Then, the required vector $\vec r$ is given by
$\vec r=λ(\vec a×\vec b)$
$⇒\vec r=λ(34\hat i+51\hat j-102\hat k)=17λ (2\hat i+3\hat j-6\hat k)$
Now, $|\vec r|=14⇒ 119|λ|=14⇒|λ|=\frac{2}{17}$
Since $\vec r$ makes an obtuse angle with y-axis. Therefore, $λ=-2/17$.
Hence, $\vec r=2(-2\hat i-3\hat j+6\hat k)$