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For the next two (02) items that follow:

Let

\left|\overset{\rightarrow}{a}\right|=7,\left|\overset{\rightarrow}{b}\right|=11,\left|\overset{\rightarrow}{a}+\overset{\rightarrow}{b}\right|=10\sqrt{3}

[NDA I 2014]

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Question : 100 of 101

Marks: +1, -0

\text{ What is }\left|\vec{a}-\vec{b}\right|\text{ equal to? }

$2\sqrt{2}$
$2\sqrt{10}$
5
10

Solution:

\left|\vec{a}+\vec{b}\right|^2=\left|\vec{a}\right|^2+\left|\vec{b}\right|^2+2\left|\vec{a}\right|\cdot\left|\vec{b}\right|\cos\theta

\Rightarrow\cos\theta=\frac{300-170}{2\times7\times11}=\frac{130}{2\times7\times11}

\left|\vec{a}-\vec{b}\right|^2=\left|\vec{a}\right|^2+\left|\vec{b}\right|^2+2\left|\vec{a}\right|\cdot\left|\vec{b}\right|\cos\theta

=170-130=40

\Rightarrow\left|\vec{a}-\vec{b}\right|=2\sqrt{10}

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