# ch2_5lecture - 3 D VECTORS(Section 2.5 Todays Objectives...

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3 – D VECTORS (Section 2.5) Today’s Objectives : Students will be able to : a) Represent a 3-D vector in a Cartesian coordinate system. b) Find the magnitude and coordinate angles of a 3-D vector c) Add vectors (forces) in 3-D space

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APPLICATIONS Many problems in real-life involve 3-Dimensional Space. How will you represent each of the cable forces in Cartesian vector form?
APPLICATIONS (continued) Given the forces in the cables, how will you determine the resultant force acting at D, the top of the tower?

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A UNIT VECTOR Characteristics of a unit vector : a) Its magnitude is 1. b) It is dimensionless. c) It points in the same direction as the original vector ( A ). The unit vectors in the Cartesian axis system are i , j , and k . They are unit vectors along the positive x, y, and z axes respectively. For a vector A with a magnitude of A, an unit vector is defined as U A = A / A .
Consider a box with sides A X , A Y , and A Z meters long. The vector A can be defined as A = ( A X i + A Y j + A Z k ) m The projection of the vector A in the x-y plane is A ´ . The magnitude of this projection, A´, is found by using the same approach as a 2-D vector: A´ = (A X 2 + A Y 2

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ch2_5lecture - 3 D VECTORS(Section 2.5 Todays Objectives...

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