What is the minimum number of coplanar vectors having different magnitudes that can be added to give a zero resultant?

The magnitude of the vector resulting from the addition of two vectors,$6\hat{i} + 7\hat{j}$ and $3\hat{i} + 4\hat{j}$,is:

If $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}+\hat{j}-4 \hat{k}$ form a right-angled triangle,then which of the following is satisfied?

If $\overrightarrow A = 2\hat i + \hat j$,$\overrightarrow B = 3\hat j - \hat k$,and $\overrightarrow C = 6\hat i - 2\hat k$,find the value of $\overrightarrow A - 2\overrightarrow B + 3\overrightarrow C$.

The resultant of two forces $3P$ and $2P$ is $R$. If the first force is doubled,then the resultant is also doubled. The angle between the two forces is ........... $^o$.

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces