If $\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors and $|\overrightarrow{a}+\overrightarrow{b}|=1$,then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

Let $u, v, w$ be vectors such that $u + v + w = 0$. If $|u| = 3, |v| = 4,$ and $|w| = 5,$ find the value of $u \cdot v + v \cdot w + w \cdot u$.

Let $A(3 \hat{i}+\hat{j}-\hat{k})$ and $B(13 \hat{i}-4 \hat{j}+9 \hat{k})$ be two points on a line $L$. $C$ and $D$ are points on $L$ on either side of $A$ at distances of $9$ and $6$ units respectively, and $C$ lies between $A$ and $B$. Then the position vectors of $C$ and $D$ are respectively:

Let $\vec{\alpha} = (\lambda - 2) \vec{a} + \vec{b}$ and $\vec{\beta} = (4\lambda - 2)\vec{a} + 3\vec{b}$ be two given vectors where $\vec{a}$ and $\vec{b}$ are non-collinear. The value of $\lambda$ for which vectors $\vec{\alpha}$ and $\vec{\beta}$ are collinear is:

If the coordinates of points $A, B, C,$ and $D$ are $(1, 2, 3), (4, 5, 7), (-4, 3, -6),$ and $(2, 9, 2)$ respectively,then the angle between $AB$ and $CD$ is:

Answer the following as true or false.
Two collinear vectors are always equal in magnitude.