The angle between vectors $\vec a$ and $\vec b$ is $\frac{\pi }{6}$. The angle between vectors $-3\vec a$ and $2\vec b$ is

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to vector $\vec{A}$,and the resultant magnitude is equal to half of the magnitude of $\vec{B}$. Then,the angle between $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of '$p$' is

For the components of a vector $\vec{A} = (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$,match the following columns.

Column $I$	Column $II$
$(A)$ Component along $x$-axis	$(p)$ $5 \text{ unit}$
$(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$	$(q)$ $4 \text{ unit}$
$(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$	$(r)$ $0$
$(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$	$(s)$ None

For the resultant of two vectors to be maximum,what must be the angle between them? $(^o)$

The position of a particle in a rectangular coordinate system is $(3, 2, 5)$. Then its position vector will be