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Vector Algebra I Two Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
10 x 2 = 20
1. If D and E are the midpoints of the sides AB and AC of a triangle ABC, prove that $\overrightarrow{BE}+\overrightarrow{DC}={3\over2}\overrightarrow{BC}$ .

2. Find a unit vector along the direction of the vector 5$\hat{i}$-3$\hat{j}$+4$\hat{k}$ .

3. Find the direction cosines of the line joining (2, 3, 1) and (3, - 1, 2).

4. Verify whether the following ratios are direction cosines of some vector or not${4\over 3}.0,{3\over 4}$

5. Find the direction cosines and direction ratios for the following vectors.5$\hat{i}$-3$\hat{j}$-48$\hat{k}$

6. If $\overrightarrow{a}$ and $\overrightarrow{b}$are two vectors such that | $\overrightarrow{a}$ |=10,| $\overrightarrow{b}$ |=15 and $\overrightarrow{a}$.$\overrightarrow{b}$ = 75 $\sqrt{2}$, find the angle between $\overrightarrow{a}$and $\overrightarrow{b}$.

7. Find the angle between the vectors  $2\hat{i}+3\hat{j}-6\hat{k}$ and $6\hat{i}-3\hat{j}+2\hat{k}$

8. Find the area of the parallelogram whose adjacent sides are $\overrightarrow{a}=3\hat{i}+\hat{j}+4\hat{k}$ and $\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}$ .

9. Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done.

10. If $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=2\hat{i}+3\hat{j}-5\hat{k}$ then find $\vec{a} \times \vec{b}$ . Verify that$\vec{a}$ and $\vec{b}$ are perpendicular to each other.