Vectors

The magnitude of the vector $\vec{a}=\left(\genfrac{}{}{0ex}{}{3}{4}\right)$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{5}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{4}{1}\right)$. The result of $\vec{a}+\vec{b}$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{5}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{4}{1}\right)$. The result of $\vec{a}-\vec{b}$ is ...

Given $\vec{p}=\left(\genfrac{}{}{0ex}{}{1}{2}\right)$. The vector $2\vec{p}$ is ...

Given points $A(1,2)$ and $B(4,6)$. The vector $\overrightarrow{AB}$ is ...

The magnitude of the vector $\vec{u}=\left(\genfrac{}{}{0ex}{}{5}{0}\right)$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{1}{3}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{4}{2}\right)$. The value of $\vec{a}\cdot \vec{b}$ is ...

The magnitude of the vector $\left(\genfrac{}{}{0ex}{}{6}{8}\right)$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{-1}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{3}{4}\right)$. The value of $\vec{a}\cdot \vec{b}$ is ...

Given points $A(-1,2)$ and $B(3,5)$. The length of $\overrightarrow{AB}$ is ...

The vector $\left(\genfrac{}{}{0ex}{}{x}{3}\right)$ is perpendicular to $\left(\genfrac{}{}{0ex}{}{2}{-4}\right)$. The value of $x$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{4}{2}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{1}{3}\right)$. The result of $3\vec{a}-2\vec{b}$ is ...

The vector $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{4}\right)$ is parallel to $\vec{b}=\left(\genfrac{}{}{0ex}{}{k}{10}\right)$. The value of $k$ is ...

Given $\vec{u}=\left(\genfrac{}{}{0ex}{}{1}{2}\right)$ and $\vec{v}=\left(\genfrac{}{}{0ex}{}{3}{-1}\right)$. The length of $\vec{u}+\vec{v}$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{3}{4}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{4}{3}\right)$. The value of $\cos \theta$, where $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{3}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{4}{-1}\right)$. The value of $(\vec{a}+\vec{b})\cdot (\vec{a}-\vec{b})$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{0}{2}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{2}{2}\right)$. The angle between $\vec{a}$ and $\vec{b}$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{3}{-2}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{-1}{4}\right)$. The result of $2\vec{a}-3\vec{b}$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{2}{-1}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{-3}{4}\right)$. The length of $\vec{a}+\vec{b}$ is ...

Given $\vec{a}=\left(\genfrac{}{}{0ex}{}{3}{4}\right)$ and $\vec{b}=\left(\genfrac{}{}{0ex}{}{-2}{1}\right)$. The value of $\vec{a}\cdot (\vec{a}+\vec{b})$ is ...