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Three slogans on chart papers are to be placed on a school bulletin board at the points A, Band C displaying A (Hub of Learning), B (Creating a better world for tomorrow) and C (Education comes first). The coordinates of these points are (1, 4, 2), (3, -3, -2) and (-2, 2, 6) respectively.

Based on the above information, answer the following questions.

1. Let $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ be the position vectors of points A, B and C respectively, then $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$ is equal to:

1. $2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}}$
2. $2\hat{\text{i}}-3\hat{\text{j}}-6\hat{\text{k}}$
3. $2\hat{\text{i}}+8\hat{\text{j}}+3\hat{\text{k}}$
4. $2(7\hat{\text{i}}+8\hat{\text{j}}+3\hat{\text{k}})$

2. Which of the following is not true?

1. $\overline{\text{AB}}+\overline{\text{BC}}+\overline{\text{CA}}=\vec{0}$
2. $\overline{\text{AB}}+\overline{\text{BC}}-\overline{\text{AC}}=\vec{0}$
3. $\overline{\text{AB}}+\overline{\text{BC}}-\overline{\text{CA}}=\vec{0}$
4. $\overline{\text{AB}}-\overline{\text{CB}}+\overline{\text{CA}}=\vec{0}$

3. Area of $\triangle\text{ABC}$ is:

1. 19 sq. units
2. $\sqrt{1937}\text{sq}.\text{units}$
3. $\frac{1}{2}\sqrt{1937}\text{sq}.\text{units}$
4. $\sqrt{1837}\text{sq}.\text{units}$

4. Suppose, if the given slogans are to be placed on a straight line, then the value of $|\vec{\text{a}}\times\vec{\text{b}}+\vec{\text{b}}\times\vec{\text{c}}+\vec{\text{c}}\times\vec{\text{a}}|$ will be equal to:

1. -1
2. -2
3. 2
4. 0

5. If $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+6\hat{\text{k}},$ then unit vector in the direction of vector $\vec{\text{a}}$ is:

1. $\frac{2}{7}\hat{\text{i}}-\frac{3}{7}\hat{\text{j}}-\frac{6}{7}\hat{\text{k}}$
2. $\frac{2}{7}\hat{\text{i}}+\frac{3}{7}\hat{\text{j}}+\frac{6}{7}\hat{\text{k}}$
3. $\frac{3}{7}\hat{\text{i}}+\frac{2}{7}\hat{\text{j}}+\frac{6}{7}\hat{\text{k}}$
4. None of these