The angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is $60^\circ$ and \(|\mathbf{a}|=2

Question

The angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is $60^\circ$ and $|\mathbf{a}|=2$, $|\mathbf{b}|=1$. Find the value of $\mathbf{a}\cdot\mathbf{b}$. By simplifying $(2\mathbf{a}-\mathbf{b})\cdot(2\mathbf{a}-\mathbf{b})$, show that $|2\mathbf{a}-\mathbf{b}|=\sqrt{13}$.

Accepted Answer

(a) $1$, (b) $\sqrt{13}$

Vectors - Magnitude of a Vector

Vectors - Magnitude of a Vector

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