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Representation of Algebraic Vectors in 2D and 3D

Learn to represent vectors algebraically by ordered pairs and triples, find magnitudes, and apply operations on vectors in 2D and 3D space. Explore unit vectors and vector addition. Practice problems included.

jeromephillips
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Representation of Algebraic Vectors in 2D and 3D

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  1. Pre-calc w-up 10/26

  2. 8.2 Algebraic Vectors • We can represent vectors algebraically by order pairs. • Since vectors with the same magnitude and direction are equal, many vectors can be represented by the same order pair. • ALL vectors on the graph are represented by • Use the < > not the usual ( ) P2(x2,y2) P1(x1,y1)

  3. Representation of a Vector as an Ordered Pair

  4. X (-3,5) Y(4,-2) Ex1: Write the order pair that represent the vector from X(-3,5) to Y(4,-2) and find the magnitude.

  5. We can represent a vector in 3-D just like we did in 2-D as an ordered triple.

  6. Ex2: Write the order triple that represents the vector from A(-2,5,8) to B(3,9,-9) and find the magnitude

  7. Operations on ordered triples are similar to operations on ordered pairs.

  8. Ex3:

  9. Ex 4:

  10. Unit vector: a vector that has a magnitude of one unit.

  11. Once you have a vector written as an ordered pair, you can write it as the sum of unit vectors. • Ex5: Write vector AB as the sum of unit vectors for A(4,-1) and B(6,2) • Write as an order pair • Write as a sum of unit vectors

  12. Assignment: 8.2 p. 497 #15 – 41 odds 8.3 pg 503 #12-14 all, 15-33 odds

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