Condition for Three Vectors to Form a Triangle

Q.

3 vectors $\overline{a},\overline{b},\overline{c}$ can always form the sides of a triangle if $\overline{a}+\overline{b}+\overline{c}=0$

1. True

2. False

Q.

The given vectors can form sides of a triangle $\hat{i}-\hat{j}-\hat{k},-2\hat{i}+3\hat{j}-\hat{k},\hat{i}-2\hat{j}+2\hat{k}$

1. True

2. False

Q. If $\overrightarrow{x}$ and $\overrightarrow{y}$ are two non-parallel vectors and $ABC$ is a triangle with side lengths $a,b$ and $c$ satisfying $(20a-15b)\overrightarrow{x}+(15b-12c)\overrightarrow{y}+(12c-20a)(\overrightarrow{x}\times \overrightarrow{y})=\overrightarrow{0}$, then triangle $ABC$ is

1. an acute-angled triangle
2. an obtuse-angled triangle
3. a right-angled triangle
4. an isosceles triangle

Q. If ABCDEF is a regular hexagon and $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \overrightarrow{AD}$, then $\lambda$ =

1. 2
2. 3
3. 4
4. 6

Q. If ABCDEF is a regular hexagon and $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \overrightarrow{AD}$, then $\lambda$ =

1. 2
2. 3
3. 4
4. 6

Q.

The given vectors can form sides of a triangle $\hat{i}-\hat{j}-\hat{k},-2\hat{i}+3\hat{j}-\hat{k},\hat{i}-2\hat{j}+2\hat{k}$

1. True

2. False