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

If $\vec{a}, \vec{b}, \vec{c}$ are position vectors of points $A, B, C$ respectively,with $2 \vec{a}+3 \vec{b}-5 \vec{c}=\vec{0}$,then the ratio in which point $C$ divides segment $AB$ is

If the points $P(4, 5, x)$,$Q(3, y, 4)$ and $R(5, 8, 0)$ are collinear,then the value of $x + y$ is

Let $|\vec{a}| = |\vec{b}| = |\vec{a} - \vec{b}| = 1$,then the angle between $\vec{a}$ and $\vec{b}$ is:

The points having position vectors $2i + 3j + 4k,$ $3i + 4j + 2k,$ and $4i + 2j + 3k$ are the vertices of:

If the angle between $\vec{a}$ and $\vec{b}$ is $30^o$,then the angle between $3\vec{a}$ and $-4\vec{b}$ will be ............ $^o$.