#### Vector Algebra I Three Marks Questions

11th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 00:45:00 Hrs
Total Marks : 30
10 x 3 = 30
1. Find the value of $\lambda$ for which the vectors $\overrightarrow{a}=3\hat{i}+2\hat{j}+9\hat{k}$ and $\overrightarrow{b}=\overrightarrow{i}+\lambda \overrightarrow{j}+3\overrightarrow{k}$ are parallel.

2. Show that the following vectors are coplanar $\hat{i}$ −2$\hat{j}$ +3$\hat{k}$,-2 $\hat{i}$ +3$\hat{j}$ - 4 $\hat{k}$ ,-$\hat{j}$ +2 $\hat{k}$ .

3. Show that the following vectors are coplanar 5$\hat{i}$ +6$\hat{j}$ +7$\hat{k}$ ,7 $\hat{i}$ -8$\hat{j}$ +9 $\hat{k}$,3$\hat{i}$+20$\hat{j}$ +5$\hat{k}$ .

4. If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$ prove that $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular.

5. For any vector $\overrightarrow{r}$ prove that $\overrightarrow{r}$ = ($\overrightarrow{r}.\hat{i}$) $\hat{i}$+ ($\overrightarrow{r}.\hat{j}$) $\hat{j}$+ + ($\overrightarrow{r}.\hat{k}$) $\hat{k}$.

6. Find the angle between the vectors $5\hat{i}+3\hat{j}+4\hat{k}$and$6\hat{i}-8\hat{j}-\hat{k}$.

7. Show that the points (4, - 3, 1), (2, - 4, 5) and (1, - 1, 0) form a right angled triangle.

8. If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are three vectors such that $\overrightarrow{a}+2\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ and $|\overrightarrow{a}|=3,|\overrightarrow{b}|=4,|\overrightarrow{c}|=7,$find the angle between $\overrightarrow{a}$and$\overrightarrow{b}$.

9. If $|\overrightarrow{a}|=5,|\overrightarrow{b}|=6,|\overrightarrow{c}|=7$ and $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c} =\overrightarrow{0}$ ,find $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$.

10. Find the cosine and sine angle between the vectors $\overrightarrow{a}=2\hat{i}+\hat{j}+3\hat{k}$ and  $\overrightarrow{b}=4\hat{i}-2\hat{j}+2\hat{k}$.