If | a | = 10 , | b | = 2 and a · b = 12 , then the value of | a × b | is:

Question

If $| \vec{a} |$ $= 10$ , $| \vec{b} |$ $= 2$ and $\vec{a} \cdot \vec{b} = 12$ , then the value of $| \vec{a} \times \vec{b} |$ is:

Smart Achievers · Accepted Answer

(4)

Ans. 16

Explanation:

Here, $| \vec{a} |$ $= 10,$ $| \vec{b} |$ $= 2$ and $\vec{a} \cdot \vec{b} = 12$ [given]

$∴$ $\vec{a} \cdot \vec{b} =$ $| \vec{a} |$ $| \vec{b} |$ $\cos θ$

$12 = 10 \times 2 \cos θ$

$\Rightarrow$ $\cos θ = \frac{12}{20} = \frac{3}{5}$

$\Rightarrow$ $\sin θ = \sqrt{1 - \cos^{2} θ}$

$= \sqrt{1 - \frac{9}{25}}$

$\Rightarrow$ $\sin θ = \pm \frac{4}{5}$

$∴$ $| \vec{a} \times \vec{b} |$ $=$ $| \vec{a} |$ $| \vec{b} |$ $| \sin θ |$

$= 10 \times 2 \times \frac{4}{5} = 16$

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