Product of Mag. of 2 vectors & cosine Scalar Quantities PQ completely described by magnitude. Can be added with simple algebraic rules.
Scalar/Dot
angle in btw OR Product of mag. of 1
Product Vector Quantities PQ described by both mag. & dir. Can be added by ∆ law of vector add.
& horizontal component of other
Presentation of a Vector #symbol (→) #Magnitude, F=|F→|
Displacement
Equal vectors mag. & dir. are same
Vector
Negative Equal mag. is same; dir. is opp.
Unit Vector(Â) mag. is 1 Â=A⇾/|A⇾|
Tells position of point with respect to origin
Position Vector acting along same or ||
Collinear Vectors
Important lines or in anti- parallel dir.
terms
Coplanar vectors vectors in the same plane
Rectangular Component in 3D
Coinitial vectors vectors with same initial points
Coterminus vectors vectors ending at same point
Resolution/
Rectangular mag.e->0; dir.-> arbitrary i.e. Same initial & final position
Components Zero/ Null vector
of Vector #A⇾±0⇾=A⇾; #(A⇾/λ).0⇾=0⇾
On multiplying vector by real no, resulting vector has
Process of splitting vector into same dir. but mag. is multiplied by that no. λxA⇾=B⇾
2 or more component vectors Resolution Multiplication
of Vector Motion in a plane of vector by Multiplying vector by negative real number flips its dir. (-λ)xA⇾=-B⇾
eg. #man walking #Lawn roller- pull easier than push real no.
If scalar multiplies vector, result is vector. F⇾=mxa⇾
Subtrac'n of vector from another = Subtraction
adding -ve of that vector to given vector of Vectors Polar vectors Vectors having starting points.
Types of Vectors
Follows commutative Law: Axial vectors vectors with no starting point; act along axis of rotation
Vector
Follows Associative Law: Addition Laws of vector Process of adding 2 or more vectors is composition/ addition
Properties addition of vectors, has 3 types: #∆ Law; # ||gm law; #Polygon law
Follows Distributive Law:
Triangle Law of If 2 sides of ∆ illustrate 2 vectors both in mag. & dir. in 1 order, 3rd side in
I [2 vectors in same direc'n]: R=P+Q , β=0 Vector Addition reverse order is resultant AB⇾+BC⇾+CA⇾=0 => P⇾+Q⇾=R⇾[CA⇾=-AC⇾]
II [2 vectors perpendicular]: Cases If 2 adjacent sides of ||gm illustrate 2 vectors both in mag. & dir. diagonal from
||gm law of same point is resultant AB⇾+BC⇾=AC⇾ => AD⇾+DC⇾=AC⇾ =>P⇾+Q⇾=R⇾
vector
III [2 vectors in opp. direc'n]: R=P-Q , β=0 addition Examples: #Bird flying #Sling
Polygon Law of If sides of open polygon illustrate no. of vectors both in mag. & dir. in 1 order,
Magnitude of Resultant(R⇾)/ vector addition closing side in reverse order is resultant (F⇾)PU⇾=A⇾+B⇾+C⇾+D⇾+E⇾
||gm law: Analytical treatment
Direc'n
Scalar/Dot
angle in btw OR Product of mag. of 1
Product Vector Quantities PQ described by both mag. & dir. Can be added by ∆ law of vector add.
& horizontal component of other
Presentation of a Vector #symbol (→) #Magnitude, F=|F→|
Displacement
Equal vectors mag. & dir. are same
Vector
Negative Equal mag. is same; dir. is opp.
Unit Vector(Â) mag. is 1 Â=A⇾/|A⇾|
Tells position of point with respect to origin
Position Vector acting along same or ||
Collinear Vectors
Important lines or in anti- parallel dir.
terms
Coplanar vectors vectors in the same plane
Rectangular Component in 3D
Coinitial vectors vectors with same initial points
Coterminus vectors vectors ending at same point
Resolution/
Rectangular mag.e->0; dir.-> arbitrary i.e. Same initial & final position
Components Zero/ Null vector
of Vector #A⇾±0⇾=A⇾; #(A⇾/λ).0⇾=0⇾
On multiplying vector by real no, resulting vector has
Process of splitting vector into same dir. but mag. is multiplied by that no. λxA⇾=B⇾
2 or more component vectors Resolution Multiplication
of Vector Motion in a plane of vector by Multiplying vector by negative real number flips its dir. (-λ)xA⇾=-B⇾
eg. #man walking #Lawn roller- pull easier than push real no.
If scalar multiplies vector, result is vector. F⇾=mxa⇾
Subtrac'n of vector from another = Subtraction
adding -ve of that vector to given vector of Vectors Polar vectors Vectors having starting points.
Types of Vectors
Follows commutative Law: Axial vectors vectors with no starting point; act along axis of rotation
Vector
Follows Associative Law: Addition Laws of vector Process of adding 2 or more vectors is composition/ addition
Properties addition of vectors, has 3 types: #∆ Law; # ||gm law; #Polygon law
Follows Distributive Law:
Triangle Law of If 2 sides of ∆ illustrate 2 vectors both in mag. & dir. in 1 order, 3rd side in
I [2 vectors in same direc'n]: R=P+Q , β=0 Vector Addition reverse order is resultant AB⇾+BC⇾+CA⇾=0 => P⇾+Q⇾=R⇾[CA⇾=-AC⇾]
II [2 vectors perpendicular]: Cases If 2 adjacent sides of ||gm illustrate 2 vectors both in mag. & dir. diagonal from
||gm law of same point is resultant AB⇾+BC⇾=AC⇾ => AD⇾+DC⇾=AC⇾ =>P⇾+Q⇾=R⇾
vector
III [2 vectors in opp. direc'n]: R=P-Q , β=0 addition Examples: #Bird flying #Sling
Polygon Law of If sides of open polygon illustrate no. of vectors both in mag. & dir. in 1 order,
Magnitude of Resultant(R⇾)/ vector addition closing side in reverse order is resultant (F⇾)PU⇾=A⇾+B⇾+C⇾+D⇾+E⇾
||gm law: Analytical treatment
Direc'n
