The value of $|\vec{a}-\vec{b}|$, if two vectors $\vec{a}$ and $\vec{b}$ are such that $|\vec{a}|=1,|\vec{b}|=4$, and $\vec{a} . \vec{b}=5$ is :
Answer & explanation
Correct answer: option 2
to find $|\vec{a}-\vec{b}|$
given $|\vec{a}|=1 \quad|\vec{b}|=4 \quad \vec{a} . \vec{b}=5$
We know that $(\vec{a}-\vec{b}) .(\vec{a}-\vec{b})=|\vec{a}-\vec{b}|^2$
$\Rightarrow |\vec{a}|^2+|\vec{b}|^2-2 \vec{a} . \vec{b}=|\vec{a}-\vec{b}|^2$
substituting the values
$\Rightarrow \left(1^2+4^2-2 \times 5\right)=|\vec{a}-\vec{b}|^2$
$\Rightarrow \sqrt{(16+1-10)}=|\vec{a}-\vec{b}|$
$|\vec{a}-\vec{b}|=\sqrt{7}$