Pradeep Kshetrapal is teaching live on Unacademy Plus
PHYSICS Class XI Pradeep Kshetrapal
Chapter 4. Motion in a plain VECTORS Lesson: XI-4-5 Concept of Unit vector
Concept of Unit Vector
Any measurable quantity in Physics is expressed as combination of two identities 1st A standard measurement of its own and 2nd Its multiplier, to show the size.
The quantity Distance- 6 Kilometer give information that 1. Our Unit of measurement is Kilometer (and not- meter, foot or mile) and 2. The distance is 6 times multiplying the standard unit. Note that: Here Kilometer has to have the same nature as of Distance. It can not be mass or time.
Similarly any vector quantity also has an arbitrary unit and a multiplier If I say my position is 5 meters south of origin, then 1 meter towards south is unit in vector but if I say my position is 8 steps south of origin then 1 step towards south is unit in vector. This unit can be made in combination as well. Like A.U., L.Y.
NOTATIONS just like a qty- number x Unit a Vector -number x Unit vector U nu Here is a unit vector of U. As per definition its magnitude is One. Its nature and direction is same as main vector
U=nu Unit Vector it-- and magnitude of vector n =- a = 6a
Universal notations for unit vectors A unit vector in direction of +x is noted as In direction of +y is noted as) -n direction of +Z is noted as k
Here vector Ax is x times unit vector hence it is Axl and its direction is in the X direction. Similarly Ay is y times unit vector hence it is yj and its direction is in the Y direction. Similarly a vector in Z direction Ag can be represented as AA Here Ar, Ay, Ag are magnitude of full vectors Ax , Ay, Az in their respective directions Ay Ayj
Vector A can be written according to triangle rule of additions as B = Bx+ By or By Byj
We can also find out unit vector of any given vector like : find unit vector of A + 2-k Magnitude of given vector is V32 + 22 122v3 Therefore according to relation u- the unit vector is K 2V3