JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q85

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MathematicsSingle correct+4 / -1Question 85 of 90

If $\vec x=3\hat i-6\hat j-\hat k$ , $\vec y=\hat i+4\hat j-3\hat k$ and $\vec z=3\hat i-4\hat j-12\hat k$ , then the magnitude of the projection of $\vec x\times\vec y$ on $\vec z$ is :

Answer and worked solution

Official answer: C

$\vec x\times\vec y=\begin{vmatrix}\hat i&\hat j&\hat k\\3&-6&-1\\1&4&-3\end{vmatrix}=22\hat i+8\hat j+18\hat k.$
$\frac{|(22,8,18)\cdot(3,-4,-12)|}{13}=\frac{|66-32-216|}{13}=14.$

Topics:Cross product Dot product

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 85