## Vector Very Short Answer Type Questions

**Question 1. We usually say that ‘time moves in a forward direction’, but time is not a vector quantity. Why?**

**Answer:** Does not obey vector algebra

**Question 2. What change takes place in the value of the resultant of two vectors when the angle between them is increased from 0 to 90°?**

**Answer:** Decreases

**Question 3. Is any physical quantity having a magnitude and a direction a vector quantity?**

**Answer:** No

**Question 4. Can the resultant of three coplanar vectors be zero?**

**Answer**: Yes

**Question 5. “If the magnitudes and directions of three forces acting on a particle are represented by three sides of a triangle taken in order, the particle remains in equilibrium”— state whether the statement is true or false.**

**Answer:** True

**Question 6. What is a free vector?**

**Answer:** Whose initial and final points are not fixed

**Question 7. What are orthogonal unit vectors?**

**Answer:** \(\hat{i}, \hat{j} \text { and } \hat{k}\) which are mutually perpendicular to each other

**Question 8. What is the position vector of the origin of a coordinate system?**

**Answer:** Zero

**Question 9. Magnitude of the resultant of two vectors is minimal when they are**

**Answer:** In the opposite direction

**Question 10. The resultant of two vectors of magnitudes 3 units and 4 units 5 units. What is the angle between the vectors?**

**Answer:** \(\frac{\pi}{2}\)

**Question 11. If an acceleration acts on a moving object along the direction of motion, the velocity of the object**

**Answer:** Increases

**Question 12. Value of the resultant of \((\vec{A}+\vec{B}) \text { and }(\vec{A}-\vec{B})\) is**

**Answer:** 2 \(\vec{A}\)

**Question 13. If \(\left|\vec{v}_1+\vec{v}_2\right|=\left|\vec{v}_1-\vec{v}_2\right| \text { and } \vec{v}_1 \text { and } \vec{v}_2\) have finite values then \(\vec{v}_1 \text { and } \vec{v}_2\) are**

**Answer:** Mutually perpendicular

**Question 14. Can commutative law be applied to vector subtraction?**

**Answer:** No

**Question 15. Can we apply associative law to vector subtraction?**

**Answer:** Yes

**Question 16. How many components can a vector be resolved into?**

**Answer:** Infinite

**Question 17. Is a rocket in flight an illustration of a projectile?**

**Answer**: No

**Question 18. What is the angle of projection for attaining maximum vertical height?**

**Answer:** 90°

**Question 19. What is the angle between two vectors whose vector product is zero?**

**Answer:** 0°

**Question 20. What is the scalar product of two vectors perpendicular to each other?**

**Answer:** 0

**Question 21. What is the angle between \((\vec{A}+\vec{B}) \text { and }(\vec{A} \times \vec{B}) \text { ? }\)**

**Answer: **90°

**Question 22. Can the value of \(\vec{A} \times \vec{A}\) be 0?**

**Answer:** Yes

**Question 23. If \(\hat{i}\) and \(\hat{j}\) are unit vectors along x and y axes respectively then the angle made by (\(\hat{i}\) + \(\hat{j}\)) vector with the x-axis is**

**Answer:** 45°

**Question 24. What is the angle between the vectors \(\vec{A} \text { and } \vec{A} \times \vec{B} \text {? }\)**

**Answer:** 90°

**Question 25. What is the angle between vector \(\vec{A}\) and the resultant of \((\vec{A}+\vec{B}) \text { and }(\vec{A}-\vec{B}) ?\)**

**Answer:** Zero

**Question 26. Skating on a circular ice slab of a radius of 200 m, three girls travel between diametrically opposite points P and Q along three different paths. Find out the magnitude of the displacement vector for each of them. For which of the girls, this magnitude is equal to the actual distance traveled by her?**

**Answer:** 400 m for each B

## Vector Assertion Reason Type Questions And Answers

These questions have statement 1 and statement 2. Of the four choices given below, choose the one that best describes the two statements.

- Statement 1 is true, statement 2 is true; statement 2 Is a correct explanation for statement 1.
- Statement 1 is true, and statement 2 is true; statement 2 is not a correct explanation for statement 1.
- Statement 1 is true, statement 2 is false.
- Statement 1 is false, and statement 2 is true.

**Question 1. Statement 1:** The minimum number of unequal vectors on a plane required to give zero resultant is three.

**Statement 2:** If \(\vec{B}+\vec{A}+\vec{C}=0\), then they must lie on the same plane.

**Answer:** 2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

**Question 2. Statement 1:** If <p is the angle between \(\vec{P}\) and \(\vec{Q}\), then \(\tan \phi=\frac{|\vec{P} \times \vec{Q}|}{\vec{P} \cdot \vec{Q}}\)

Statement 2. Statement 1 is true, statement 2 is false.

**Answer:** 2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

**Question 3. Statement 1:** If two vectors \(\vec{a}\), and \(\vec{b}\), are such that \(|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|\), then the angle between \(\vec{a}\) and \(\vec{b}\) is 90°.

**Statement 2:** \(\vec{a}+\vec{b}=\vec{b}+\vec{a}\).

**Answer:** 2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

**Question 4. Statement 1:** A physical quantity cannot be called a vector if its magnitude is zero.

**Statement 2:** A vector has both magnitude and direction.

**Answer:** 4. Statement 1 is false, statement 2 is true.

**Question 5. Statement 1:** Finite angular displacement is not a vector quantity.

**Statement 2:** A vector must obey the proper law of addition.

**Answer:** 1. Statement 1 is true, statement 2 is true; statement 2 Is a correct explanation for statement 1.

**Question 6. Statement 1:** The vector sum of two vectors is always greater than their vector difference.

**Statement 2:** If \(\vec{A}\) and \(\vec{B}\) are perpendicular to each other, the magnitudes of \(\vec{A}\) + \(\vec{B}\) and \(\vec{A}\)–\(\vec{B}\) are the same.

**Answer:** 4. Statement 1 is false, statement 2 is true.

**Question 7. Statement 1:** (Ax B)- (BxA) is -A²B²sin²θ. Here d is the angle between A and B.

**Statement 2:** (A x B) and (B x A) are two antiparallel vectors provided A and B are neither parallel nor antiparallel.

**Answer:** 1. Statement 1 is true, statement 2 is true; statement 2 Is a correct explanation for statement 1.

**Question 8. Statement 1**: The horizontal range of a projectile is the same for angles 30° and 60° of projection.

**Statement 2:** The horizontal range of the projectile is independent of the angle of projection.

**Answer:** 3. Statement 1 is true, statement 2 is false.

**Question 9. Statement 1:** During the flight of a projectile, the horizontal component of its velocity remains uniform.

**Statement 2:** The vertical component of the velocity of a projectile becomes zero at the highest point of its path.

**Answer:** 2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

**Question 10. Statement 1:** Two orthogonal components of a force of magnitude 25 N may be 24 N and 7N.

**Statement 2:** If \(\quad|\vec{A}|=|\vec{B}|=1, |\vec{A} \times \vec{B}|^2+|\vec{A} \cdot \vec{B}|^2=1\)

**Answer:** 2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.

**Question 11. Statement 1:** The angle between the vectors \(\vec{A}=\hat{i}+\hat{j}\) and \(\vec{B}=\hat{j}+\hat{k} \text { is } \frac{\pi}{3}\)

**Statement 2:** The angle between vector \(\vec{A}\) and \(\vec{B}\) is, \(\theta=\cos ^{-1}\left(\frac{\vec{A} \cdot \vec{B}}{A B}\right)\)

**Answer:** 1. Statement 1 is true, statement 2 is true; statement 2 Is a correct explanation for statement 1.

**Question 12. Statement 1:** The initial velocity of projectile = (a\(\hat{i}\)+b\(\vec{j}\)). The horizontal range becomes maximum for a = b.

**Statement 2:** for the same magnitude of initial velocity, the horizontal range of a projectile becomes maximum for the angle 45° of projection.

**Answer:** 4. Statement 1 is false, statement 2 is true.