Classify the following as scalar or vector quantities:
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Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $|\vec{a}-\vec{b}|^{2}+|\vec{a}-\vec{c}|^{2}=8$. Then $|\vec{a}+2\vec{b}|^{2}+|\vec{a}+2\vec{c}|^{2}$ is equal to

If $|a| + |b| = |c|$ and $a + b = c$,then the angle between $a$ and $b$ is

If unit vectors $\bar{a}$ and $\bar{b}$ are perpendicular to each other and a unit vector $\bar{c}$ makes an angle $\theta$ with both $\bar{a}$ and $\bar{b}$,and $\bar{c} = \alpha \bar{a} + \beta \bar{b} + r(\bar{a} \times \bar{b})$,then:

If the angle between two vectors $\vec{u} = i + k$ and $\vec{v} = i - j + ak$ is $\pi / 3,$ then the value of $a$ is:

For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying $|\vec{a}-\vec{b}|^{2}+|\vec{b}-\vec{c}|^{2}+|\vec{c}-\vec{a}|^{2}=9$ and $|2\vec{a}+k\vec{b}+k\vec{c}|=3$,the positive value of $k$ is: