Question

If $|\overrightarrow{a}|=10,|\overrightarrow{b}|=2$ and $\overrightarrow{a}.\overrightarrow{b}=12$ , then what is the value of $|\overrightarrow{a}\times \overrightarrow{b}|$ ?

• A. 12
• B. 16
• C. 20
• D. 24

Answer 1

The correct option is B 16

If any two vectors $a,b$ exist, then

value of dot product $a.b$ is $|a.b|=|a||b|\cos A$

$A$ is the angle between them.

Given $|a|=10$ and $|b|=2$

and $|a.b|=12$

$\Rightarrow |a||b|\cos A=12\Rightarrow \cos A=\frac{12}{2\times 10}=\frac{3}{5}\sin A=\sqrt{1-{\left(\frac{3}{5}\right)}^2}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=\frac{4}{5}$

Value of $|a\times b|=|a||b|\sin A=10\times 2\times \frac{4}{5}=16$