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AS/A Level Physics Scalars and vectors Study Notes | IITian Academy

AS/A Level Physics Scalars and vectors Study Notes 2025-2027 Syllabus

AS/A Level Physics Scalars and vectors Study Notes

AS/A Level Physics Scalars and vectors Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics  Study Notes syllabus with Candidates should be able to:

  1. Understand the difference between scalar and vector quantities and give examples of scalar and vector quantities included in the syllabus
  2. add and subtract coplanar vectors
  3. represent a vector as two perpendicular components

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1.4.1—understand the difference between scalar and vector quantities and give examples of scalar and vector
quantities included in the syllabus

  •  A quantity described using a magnitude and a unit is called a scalar. 
  • Vectors, on the other hand, are described using a direction along with magnitude and unit.
  • A vector is represented using an arrow above its symbol. Example, \(\overrightarrow{v}\).

1.4.2—Add and subtract coplanar vectors

  •  Vectors cannot be added or subtracted numerically based only on their magnitude.
  • The direction of a vector is taken into consideration while doing any mathematical operation.
  • Vector addition is simply finding the resultant of a number of vectors acting on a body.
  • NOTE: parallel vectors can be added arithematicaly.
  • Simplest vector addition can be done geometrically using Triangle Law.
  • For adding vectors 1 and 2: (STEP 1) Draw a line AB representing vector \(\overrightarrow{A}\) with O as the tail and P as the head. 
  • STEP 2: Draw another line BC representing vector \(\overrightarrow{B}\) with P as the tail and Q as the head. 
  • STEP 3: Now join the line AC with O as the tail and Q as the head. The line AC represents the resultant sum of the vectors \(\overrightarrow{A}\) and \(\overrightarrow{B}\).                                                                                                                         
                                                                       
  • The angle between the two vectors is calculated as \(tan (\phi) = \frac{B sin (\phi) }{A + B sin (\phi)}\). 
  • Consider this example, adding two vectors with magnitude 3 cm and 4.24cm.

       STEP 1:        STEP 2:                                                                                           STEP 3:

  • Subtraction of vectors is similar to addition except that negative magnitude needs to be considered.
  •  Example, \(\overrightarrow{A} – \overrightarrow{B} = \overrightarrow{A} + \overrightarrow{(-B)}\).
  • In this case, reverse the direction of the negative vector and perform addition.
  • When 3 or more vectors need to be added, the same principles apply, provided the vectors are all on the same plane i.e. coplanar

                                                                                        

 
 
 

1.4.3—Represent a vector as two perpendicular components

  • A given vector can be resolved into two perpendicular components based on the angle it makes with the horizontal.
  • It is the reverse of using Pythagoras’ theorem to add two perpendicular vectors, and so adding the two components will give the
    original vector.
  • The x- component is obtained via multiplying the magnitude with the cosine of the angle.
  • The y- component is obtained via multiplying the magnitude with the sine of the angle.

                                                                                            

  • NOTE : The components need not be necessarily horizontal and vertical but can exist at any angle. However, they will still remain perpendicular to each other.

 
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