Scalar and Vector | Assignment

Assignment 1:

1. If $B$ is added to $A$, under what condition does the resultant vector have a magnitude equal to $A + B$? Under what conditions are the resultant vector equal to zero?

2. State triangle law of vector addition. Obtain an expression for the resultant of two vectors $P$ and $Q$ inclined at angle $\theta$.

 

3. State the parallelogram law of vector addition. Derive the magnitude and direction of the resultant vector.

4. Can the sum of two equal vectors be equal to either of the vectors? Explain.

Assignment 2:

 

1. If the scalar product of two vectors is equal to the magnitude of their vector product, find the angle between them.

 

2. The magnitude of two vectors are equal and the angle between them is $\theta$. Show that their resultant divides angle $\theta$ equally. 

 

3. If B is added to A, under what condition does the resultant vector have a magnitude equal to A + B? under what conditions is the resultant vector equal to zero.

 

4. Two vectors $\vec{A}$ and $\vec{B}$ are such that $\vec{A} - \vec{B} = C$ and $A - B = C$. Find the angle between them.

5. If  $\widehat{i}$, $\widehat{j}$ and $\widehat{k}$ are unit vectors along $x, y,z - $ axis respectively. Find $\widehat{i}$ . ($\widehat{j}$ $\times$ $\widehat{k}$).

6. A force (in Newton) expressed in vector notation as $\vec{F} = 2 \widehat{i} + \widehat{j} - 3 \widehat{k}$ is applied on a body so that the displacement produced in meter is given by $\vec{D} = \widehat{i} - 2 \widehat{j} - 3 \widehat{k}$. Express the result and nature of the work done.

7. Given two vectors $\vec{A} = 4 \widehat{i} + 3 \widehat{j}$ and $\vec{B} = 5 \widehat{i} - 2 \widehat{j}$. Find the magnitude of each vector.

8. Can the walking of the person be an example of resolution of vector?

9. Show that the flight is an example of composition of vectors.

10. Find the unit vector of  $3 \widehat{i} + 7\widehat{j} - \widehat{k}$

 

Return to Main Menu