Find the values of $x$ and $y$ so that the vectors $2 \hat{i} + 3 \hat{j}$ and $x \hat{i} + y \hat{j}$ are equal.

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

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 ............ $^o$.

Classify the following as scalar or vector quantity:
distance

If the position vector of one end of a line segment $AB$ is $2i + 3j - k$ and the position vector of its midpoint is $3(i + j + k)$,then what is the position vector of the other end?

If the vectors $\vec{AB} = \hat{i} + 3\hat{j} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} + \hat{j} + 2\hat{k}$ are two sides of a triangle $ABC$,whose centroid is $G$,then $|\vec{AG}| = $