Solved Numerical Examples | Chapter 2 | Vectors | Physics 11th | National Book Foundation New Book

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Q. Encircle the correct option.
The number of perpendicular components of a force (in 2-D) are:
(a) 1 (b) 2 (c) 3 (d) 4
j ̂×i ̂=________
(a) 0 (b) 1 (c) k ̂ (d) -k ̂
A force of 10N is making an angle of 30° with the horizontal. Its X-components will be:
(a) 4N (b) 5N (c) 7N (d) 8.7N
If two forces of magnitude 3N and 4N are acting at right angle to each other than their resultant force will be:
(a) 7N (b) 5N (c) 1N (d) Null vector
Angle between two vectors A and B can be easily determined by:
(a) dot product (b) cross product (c) head to tail rule (d) right hand rule
For which angle the equation |A ⃗.B ⃗ |=|A ⃗×B ⃗ | is correct?
(a) 30° (b) 45° (c) 60° (d) 90°
If the cross product of two vectors vanishes, what will you say about their orientation?
Find the dot product of unit vectors with each other at (a) 0° and (b) 90°.
Show that scalar product obeys commutative property.
Solve by using the properties of dot and cross product: (a) i ̂.(j ̂×k ̂) (b) j ̂×(j ̂×k ̂)?
(a) i ̂.(j ̂×k ̂)
(b) j ̂×(j ̂×k ̂)
If both the dot product and the cross product of two vectors are zero. What would you conclude about the individual vectors?
What are rectangular components of a vector? How they can be found?
Give at least one examples for each of the scalar and vector product.
Show that: A.B=A_x B_x+A_y B_y+A_z B_z.
What units are associated with the unit vectors i ̂,j ̂ and k ̂?
Explain the resolution of a vector into its rectangular components?
What is scalar product, explain? Also write the properties of scalar product.
What is vector product, explain? Also write the properties of vector product.
What geometric interpretation does the cross product have? Explain with the help of diagram.
If the magnitude of cross product between two vectors is √3 times the dot product, find angle between them.
A force is acting on a body making an angle of 30° with the horizontal. The horizontal component of the force is 20N. Find the force.
A vector having magnitude 5.5N makes 10° with x-axis and vector r ⃗ with magnitude 4.3m makes 80° with x-axis. What is the magnitude of their dot and cross products?
The magnitude of dot and cross product of two vectors are 6√3 and 6 respectively. Find the angle between vectors.
2.1 Fatima is pulling her trolley bag while climbing up the ramp at her school gate. Find the force with which she is pulling her bag, if x-component and y-component of her force are 12N and 5N, respectively.
2.2 If vectors 𝑨=𝟓𝒊 ̂+𝒋 ̂ and 𝑩=𝟐𝒊 ̂+𝟒𝒋 ̂, then find:
(1) Projection of A on B. (ii) projection of B on A.
2.3 Two vectors A and B having magnitude 3.2 unit and 5.2 unit respectively, making an angle of 𝟔𝟎° with each other. Wat is the magnitude of their cross products?
2.1 A peddler is pushing a trolley on a horizontal road with a force of 𝟓𝟎𝑵 making 𝟑𝟎° with the road. Find the horizontal and vertical components of the force.
2.2 Find the power delivered by the engine for attaining velocity (𝟑, 𝟒)𝒎/𝒔, while it exerts a force (𝟖, −𝟐)𝑵.
2.3 Find the area of the parallelogram whose adjacent sides are given by the vectors:
𝑨=𝒊 ̂+𝟔𝒋 ̂+𝟐𝒌 ̂m and 𝑩=𝟕𝒊 ̂+𝒋 ̂+𝟓𝒌 ̂m