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1.1 Unit Vectors 1. Find the unit vector in the direction w⃗= (5,2). Solution: A unit vector in physics is defined as a dimensionless vector whose magnitude is exactly 1. A unit vector that points in the direction of A⃗is determined by formula Aˆ = A⃗ |A⃗| Where |A|is the magnitude of the vector A⃗with the following formula |A⃗|= q ...
We can add vectors in any order we want: A+B = B+A. We say that vector addition is “commutative”. We express vectors in component form using the unit vectors i, j and k, which each have magnitude 1 and point along the x, y and z axes of the coordinate system, respectively.
A unit vector is a dimensionless vector one unit in length used only to specify a given direction. Unit vectors have no other physical significance. In Physics 2110 and 2120 we will use the symbols i, j, and k (if there is a third dimension, i.e a “z” direction), although in many texts the symbols x^, y^, and z^ are often used.
Some guidelines. Identify the relevant concepts. Set up the problem. Execute the solution (i.e., do the math) Evaluate your answer (i.e., Does it make sense? Can you do a consistency check?) 3 Standards and Units.
Let xˆ be a vector of unit magnitude pointing in the positive x-direction, yˆ, a vector of unit magnitude in the positive y -direction, and z ˆ a vector of unit magnitude in the positive z - direction.
Example. Write the polar unit vectors r and θ in terms of the Cartesian unit vectors x and y . Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction.
A unit vector is denoted by a small “carrot” or “hat” above the symbol. For example, represents the unit vector associated with the vector . To calculate the unit vector associated with a particular vector, we take the original vector and divide it by its magnitude. In mathematical terms, this process is written as: Definition: A unit ...
