Vector Algebra Introduction -1

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For CBSE XII std

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By: liyakathussainhu (66 month(s) ago)

Dear Sir, pl send us this ppt,I am appearing for interview and would like to present this. liyakat.hussain@piaggio.co.in

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Vector Algebra :

Vector Algebra By D.Vasu Raj, Introduction Part-1

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A B DISTANCE AND DISPLACEMENT C D E F Distance is the trace of your travel path from A to F which is AB + BC + CD +DE +EF Displacement is the measure at its position from the beginning to end. which is

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Y-Z PLANE X-Y PLANE X-Z PLANE X Y Z The three planes x-y plane, y-z plane and x-z plane forms the three dimensional plane. The intersection of these planes forms three mutually perpendicular axis.

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X Y Z O ( 0,b,c ) ( a,b,0 ) ( a,0,0 ) ( 0,0,c ) ( 0,b,0 ) ( a,0,c ) Consider a cube of side ‘a’ units as follows. Observe the co-ordinates marked ( a,b,c )

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X Y Z LINE VECTOR: Vector representation of a line(path) A B

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X Y Z Multiplying a vector by a Scalar  the scalar times the magnitude. Negative scalar changes the direction of the vector.

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X Y Z EQUAL AND NEGATIVE VECTORS: Any vector(s) of same direction and of equal magnitude drawn any where in space are called as equal vectors. If the direction is exactly opposite then it is called as negative of that vector

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X Y Z 5 UNIT VECTOR: Vector in the same direction whose magnitude is 1 unit.

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X Y Z A B C VECTOR ADDITION(Triangular Law):

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X Y Z A B C ZERO VECTOR OR NULL VECTOR

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X Y Z A B C O VECTOR REPRESENTATION OF A POINT(Position Vector): Any point (or) Group of points can be represented as a vector from a reference point (or) ORIGIN (In Two or Three dimensional co-ordinates)

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X Y Z A B C Line vector using position vectors

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X Y Z O M Consider the unit vectors along the co-ordinate axes as follows. Let M be a point on Y- axis such that OM = b units O

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X Y Z N O M ( 0,b,c ) ( a,b,c ) ( a,b,0 ) ( a,0,0 ) ( 0,0,c ) ( 0,b,0 ) ( a,0,c ) P Consider a cube of side ‘a’ units as follows. Observe the co-ordinates marked

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X Y Z N O M P A Representation of Vector in 3- dimensional space VECTOR Consider a cuboid of size x,y,z x y z y z

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X Y Z N O P A M Representation of Vector in 3- dimensional space MODULUS

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X Y Z N O P A DIRECTION COSINES: This gives the direction of any vector by defining the cosine ratio of the angle inclined by the vectors With the co-ordinate axes.    M

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WILL BE CONTINUED BY D. VASU RAJ, M.Sc., B.Ed., CHENNAI, TAMIL NADU (any suggestions write to) vraj626@gmail.com

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