JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q85

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MathematicsSingle correct+4 / -1Question 85 of 90

If $|\vec c|^2=60$ and $\vec c\times\left(\hat i+2\hat j+5\hat k\right)=\vec0$ , then a value of $\vec c\cdot\left(-7\hat i+2\hat j+3\hat k\right)$ is :

4\sqrt2

12\sqrt2

Answer and worked solution

Official answer: D

$\vec c$ is parallel to $(1,2,5)$ : $\vec c=t(1,2,5)$ with $30t^2=60$ , so $t=\pm\sqrt2$ .
$\vec c\cdot(-7,2,3)=t(-7+4+15)=12t=\pm12\sqrt2.$
A value is $12\sqrt2$ .

Topics:Cross product Dot product

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 85