Let $ABC$ be a triangle. Let $u = \vec{AB}$ and $v = \vec{AC}$. If $D$ is the midpoint of $BC$,then $\vec{AD} =$

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{3}$ and $(\vec{a}+\vec{b}+\vec{c})^2+(\vec{b}+\vec{c}-\vec{a})^2+(\vec{c}+\vec{a}-\vec{b})^2=36$,then $|2 \vec{a}-3 \vec{b}+2 \vec{c}|^2=$

If $\vec{a} + 5\vec{b} = \vec{c}$ and $\vec{a} - 7\vec{b} = 2\vec{c}$,then which of the following is true?

Find a vector in the direction of vector $\vec{a} = \hat{i} - 2\hat{j}$ that has magnitude $7$ units.

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors,then what is the maximum value of $|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2$?

Classify the following as scalar or vector quantities:
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