The magnitude of the projection of the vector $\vec{a} = -\hat{i} + 2\hat{j} - \hat{k}$ on the unit vector $\hat{i}$ is . . . . . . .

If the position vectors of the points $A, B, C$ are $a, b, 3a - 2b$ respectively,then the points $A, B, C$ are

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec{a} + 3\vec{b}$ is collinear with $\vec{c}$ and $\vec{b} + 2\vec{c}$ is collinear with $\vec{a}$,then find the value of $\vec{a} + 3\vec{b} + 6\vec{c}$.

If $a = 3i - 2j + k$,$b = 2i - 4j - 3k$ and $c = -i + 2j + 2k$,then $a + b + c$ is

If the sum of two unit vectors is a unit vector,then the magnitude of their difference is

If $a, b, c$ are non-collinear vectors such that for some scalars $x, y, z,$ $xa + yb + zc = 0,$ then