JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q85

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MathematicsSingle correct+4 / -1Question 85 of 90

Let $\vec a$ and $\vec b$ be two unit vectors such that $|\vec a+\vec b|=\sqrt3$ . If $\vec c=\vec a+2\vec b+3(\vec a\times\vec b)$ , then $2|\vec c|$ is equal to :

\sqrt{55}

\sqrt{51}

\sqrt{43}

\sqrt{37}

Answer and worked solution

Official answer: A

$|\vec a+\vec b|^2=2+2\vec a\cdot\vec b=3$ , so $\vec a\cdot\vec b=\frac12$ and $|\vec a\times\vec b|^2=\frac34$ .

$\vec a\times\vec b$ is perpendicular to both, so
$|\vec c|^2=|\vec a+2\vec b|^2+9\cdot\frac34=(1+4+2)+\frac{27}4=\frac{55}4,$
and $2|\vec c|=\sqrt{55}$ .

Topics:Cross product Dot product

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 85