Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $?

Given $\vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k})$,$\vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k})$. The value of $(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

If $\overrightarrow A = 2\widehat i + 3\widehat j + 4\widehat k$ and $\overrightarrow B = \widehat i - \widehat j + \widehat k$,find their subtraction $\overrightarrow A - \overrightarrow B$ using the algebraic method.

The magnitude of the $X$ and $Y$ components of $\vec{A}$ are $7$ and $6$ respectively. Also,the magnitude of the $X$ and $Y$ components of $\vec{A} + \vec{B}$ are $11$ and $9$ respectively. What is the magnitude of $\vec{B}$?

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

Match Column-$I$ with Column-$II$.

Column-$I$	Column-$II$
$(1)$ Resultant of two vectors is maximum	$(a)$ $180^o$
$(2)$ Resultant of two vectors is minimum	$(b)$ $90^o$
	$(c)$ $0^o$