# Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2

Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2. Concept of Physics. Step by Step Solution of Questions for short answer of Ch-2 Physics and Mathematics. Visit official Website CISCE for detail information about ISC Board Class-11 Physics.

## Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2

Board | ISC and other board |

Publications | Bharti Bhawan Publishers |

Ch-2 | Physics and Mathematics |

Class | 11 |

Vol | 1st |

writer | H C Verma |

Book Name | Concept of Physics |

Topics | Solution of Question for short answer |

Page-Number | 27,28 |

-: Select Topics :-

Question for Short Answer

** Physics and Mathematics HC Verma Que for Short Ans Vol-1 Ch-2 Concept of Physics**

#### (page-27)

**Question 1 :-**

Is a vector necessarily changed if it is rotated through an angle?

**Answer 1 :-**

Yes. A vector is defined by its magnitude and direction, so a vector can be changed by changing its magnitude and direction. If we rotate it through an angle, its direction changes and we can say that the vector has changed.

**Question 2:-**

Is it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?

**Answer 2:**

No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.

Example: Let us add two vectors **𝐴 ⃗** and ** B ⃗** of unequal magnitudes acting in opposite directions. The resultant vector is given by

R= √A²+B²+2ABcosθ

If two vectors are exactly opposite to each other, then

θ = 180º,cos180º = −1

R = √A²+B²−2AB

⇒ R= √(A−B)²

⇒ R= (A−B) or (B−A)

**𝐴 ⃗**and

**are equal (A = B) and both are acting in the opposite directions.**

*B*⃗Yes, it is possible to add three vectors of equal magnitudes and get zero.

Lets take three vectors of equal magnitudes

**𝐴 ⃗ ,**and

*B*⃗*C*⃗ ,given these three vectors make an angle of 120º with each other. Consider the figure below:

So, along the x – axis , we have:

Hence, proved.

**Question 3 :-**

Does the phrase “direction of zero vector” have physical significance? Discuss it terms of velocity, force etc.

**Answer 3 :-**

A zero vector has physical significance in physics, as the operations on the zero vector gives us a vector.

For any vector **𝐴 ⃗** , assume that

The significance of a zero vector can be better understood through the following examples:

The displacement vector of a stationary body for a time interval is a zero vector.

Similarly, the velocity vector of the stationary body is a zero vector.

When a ball, thrown upward from the ground, falls to the ground, the displacement vector is a zero vector, which defines the displacement of the ball.

**Question 4 :-**

Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?

**Answer 4 :-**

Yes we can add three unit vectors to get a unit vector.

No, the answer does not change if two unit vectors are along the coordinate axes. Assume three unit vectors iˆ, −iˆ and jˆ along the positive *x*-axis, negative *x*-axis and positive *y-*axis, respectively. Consider the figure given below:

The magnitudes of the three unit vectors ( iˆ, −iˆ and jˆ ) are the same, but their directions are different.

So, the resultant of iˆ and −iˆ is a zero vector.

–> Now, jˆ + 0**⃗** = jˆ (Using the property of zero vector)

∴ The resultant of three unit vectors ( iˆ ,−iˆ and jˆ ) is a unit vector ( jˆ ).

**Page no 28 –**

**Question 5 :-**

Can we have physical quantities having magnitude and direction which are not vectors?

**Answer 5 :-**

Yes, there are physical quantities like electric current and pressure which have magnitudes and directions, but are not considered as vectors because they do not follow vector laws of addition.

**Question 6 :-**

(a) Two forces are added using triangle rule because force is a vector quantity.

(b) Force is a vector quantity because two forces are added using triangle rule.

**Answer 6 :-**

Two forces are added using triangle rule, because force is a vector quantity. This statement is more appropriate, because we know that force is a vector quantity and only vectors are added using triangle rule.

**Question 7 :-**

Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?

**Answer 7 :-**

No, we cannot add two vectors representing physical quantities of different dimensions. However, we can multiply two vectors representing physical quantities with different dimensions.

**Example: Torque,**

**Question 8 :-**

Can a vector have zero component along a line and still have nonzero magnitude?

**Answer 8 :-**

Example: Consider a two dimensional vector 2iˆ + 0jˆ . This vector has zero components along a line lying along the Y-axis and a nonzero component along the X-axis. The magnitude of the vector is also nonzero.

Now, magnitude of 2iˆ + 0jˆ

**Question 9 :-**

Let ε_{1} and ε_{2} be the angles made by **𝐴 ⃗** and –**𝐴 ⃗** with the positive *X*-axis. Show that tan ε_{1} = tan ε_{2}_{.} Thus, giving tan ε does not uniquely determine the direction of **𝐴 ⃗**.

**Answer 9 :-**

The direction of – **𝐴 ⃗** is opposite to **𝐴 ⃗**.So, if vector **𝐴 ⃗** and −**𝐴 ⃗** make the angles ε_{1} and ε_{2} with the X-axis, respectively, then ε_{1} is equal to ε_{2} as shown in the figure:

Here, tan ε_{1} = tan ε_{2}

Because these are alternate angles.

Thus, giving tan ε does not uniquely determine the direction of −**𝐴 ⃗**.

**Question 10 :-**

Is the vector sum of the unit vectors *i ***⃗** and *i ⃗* a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?

**Answer 10 :-**

No, the vector sum of the unit vectors *i ***⃗** and *i ***⃗** is not a unit vector, because the magnitude of the resultant of *i ***⃗** and *j* **⃗ ** is not one.

Magnitude of the resultant vector is given by

Yes, we can multiply this resultant vector by a scalar number 1/√2 to get a unit vector.

**Question 11 :-**

**Answer 11 :-**

**Question 12 :-**

Can you have **𝐴 ⃗ **× ** B ⃗ **=

**𝐴 ⃗**⋅

**with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?**

*B*⃗**Answer 12 :-**

No, we cannot have **𝐴 ⃗ **× ** B ⃗ **=

**𝐴 ⃗**⋅

**with A ≠ 0 and B ≠ 0. This is because the left hand side of the given equation gives a vector quantity, while the right hand side gives a scalar quantity. However, if one of the two vectors is zero, then both the sides will be equal to zero and the relation will be valid.**

*B*⃗**Question 13 :-**

**Answer 13 :-**

If **𝐴 ⃗ **× ** B ⃗** = 0, then both the vectors are either parallel or antiparallel, i.e., the angle between the vectors is either 0∘ or 180∘.

**𝐴 ⃗ B ⃗ **sin θ nˆ=0……… (∵ sin0º=sin180º=0)

Both the conditions can be satisfied:

(a) **𝐴 ⃗ **= ** B ⃗ **, i.e., the two vectors are equal in magnitude and parallel to each other

(b) **𝐴 ⃗ **≠ ** B ⃗ **, i.e., the two vectors are unequal in magnitude and parallel or anti parallel to each other.

**Question 14 :-**

**Answer 14 :-**

— : End of **Physics and Mathematics **HC Verma Que for Short Ans :–

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