Given $\mathbf{a}$ is a unit vector and $\mathbf{b}$ is a vector such that \(|\mathbf{

Question

Given $\mathbf{a}$ is a unit vector and $\mathbf{b}$ is a vector such that $|\mathbf{b}|=3$, and that the angle between $\mathbf{a}$ and $\mathbf{b}$ is $\theta=30^\circ$, find the value of $\mathbf{a}\cdot\mathbf{b}$ in exact form. Another vector $\mathbf{c}$ is such that $\mathbf{c}=\mathbf{a}-\mathbf{b}$. Find the exact magnitude of $\mathbf{c}$.

Accepted Answer

(i) $\frac{3\sqrt{3}}{2}$ (ii) $|\mathbf{c}| = \sqrt{10 - 3\sqrt{3}}$

Vectors - Magnitude of a Vector

Vectors - Magnitude of a Vector

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