VECTORS
IMPORTANT QUESTIONS OF PAST PAPERS
1. With the help of diagram define negative vector and resultant vector. ( 2017)
2. With the help of rectangular components of a derive vector equation for the resultant vector. (2016)
3. With the help of graphical method add two vector A and B. (2015)
4. Define resolution of vector and resolve of vector into its components. (2014)
5. Define vector and scalar quantities with two examples each. ( 2012)
6. Define resolution of vector and write down two formulas of rectangular components. (2011)
7. If Fx and Fy are the horizontal and vertical components of vector F, write down the formulas for F, show Fx and Fy by a diagram. (2010)
8. Define resolution of vector how is vector resolve into its components vectors. (2009)
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IMPORTANT SYMBOLS:
• Force= F
• Angle= 𝜽
• Horizontal Component= Fx
• Vertical Component= Fy
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IMPORTANT FORMULA’S:
1. Fx= F cos 𝜽
2. Fy=F Sin 𝜽
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Questions / Answers
Q.1: Define vector and scalar quantities with two examples each.
Ans:Scalar quantity: Physical quantities, which are completely specified by their magnitude only, are called scalar quantities. It is denoted by — .
Example: Time, Mass, Distance, Work, Energy, Temperature, Momentum etc.
Vector quantity: Physical quantities, which are completely specified by their magnitude and direction both, are called vector quantities. It is denoted by →.
Example: Displacement, Velocity, Acceleration, Force, Weight, Torque etc.
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Q.2: With the help of diagram define negative vector and resultant vector.
Ans: NEGATIVE VECTOR: A vector having the same magnitude as that of a given but opposite in direction is called negative of vector.
Diagram:
A ↑ ↓ -A
2cm 2cm
RESULTANT VECTOR: A vector which joins the tail of first vector to the head of the last vector is called the Resultant Vector.
➡️ ➡️ ➡️
R =A + B
Diagram:
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Q.3: With the help of graphical method add two vectors A and B. Describe the addition of vector by Head-To-Method.
Ans: ADDITION OF TWO VECTOR GRAPHICALLY:
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Q. 4: Describe subtraction of vectors.
Ans:SUBTRACTION OF VECTORS:
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Q.5: Define multiple of a vector with an example.
Ans:MULTIPLICATION OF VECTOR:
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Q. 6: Define resolution of vector and resolve of vector into its components.
> Ans: RESOLUTION OF VECTORS: T
The process of splitting of a vector into parts (components) is called resolution of vector.
Explanation: Consider a vector F, which make an angle ɵ with x-axis represented by the line OB. From point B draw a perpendicular BA on x-axis. In this way we get two components of OA and OB. The component OA which is long x-axis is called horizontal component of vector F and denoted by Fx. the component AB which is parallel to y-axis is called vertical component of vector F and denoted by Fy.
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Q.7: Describe addition of rectangular component of a vector and derive the expression for magnitude and direction of resultant vector?
Ans:Addition of Rectangular Components of Vector:
Rectangular components of vector (components that are perpendicular to each other) can be joining together to form resultant or original vector.
Consider right angle triangle ABC
Fx = AB = base
Fy = BC = perpendicular
F = AC = hypotenuse
FOR MAGNITUDE OF RESULTANT VECTOR:
For magnitude of vector by using Pythagoras
(H)2 = (B)2 + (P)2
(AC)2 = (AB)2 + (BC)2
F2 = (Fx)2 + (Fy)2
F = Fx2+ Fy2
F = √ (Fx)2 + (Fy)2
DIRECTION OF RESULTANT VECTOR:
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Prepared by: Sir Waseem
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