If three points $A$,$B$,and $C$ have position vectors $(1, x, 3)$,$(3, 4, 7)$,and $(y, -2, -5)$ respectively and if they are collinear,then $(x, y)$ is

In the given figure,identify which of the vectors are coinitial.

Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{i}+2 \hat{j}+\hat{k}$,$\hat{i}+2 \hat{j}+2 \hat{k}$ and $2 \hat{i}+\hat{j}+2 \hat{k}$ respectively. Let $l_1, l_2$ and $l_3$ be the lengths of perpendiculars drawn from the orthocenter of the triangle on the sides $AB, BC$ and $CA$ respectively,then $l_1^2+l_2^2+l_3^2$ equals:

If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel,then $\lambda$ is

What should be added to the vector $a = 3i + 4j - 2k$ to obtain the resultant vector $i$?

$a$ and $b$ are two non-collinear vectors,then $xa + yb$ (where $x$ and $y$ are scalars) represents a vector which is