Warm-Up Outside a room there are three light switches. One of the switches is connected to a light bulb inside the room. Each of the three switches can.

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Presentation transcript:

Warm-Up Outside a room there are three light switches. One of the switches is connected to a light bulb inside the room. Each of the three switches can be either “ON” or “OFF”. You are allowed to set each switch the way you want and then enter the room (so, you can only enter the room once). The question is, which switch controls the bulb?

Let’s clear something up… A vector can be written in two forms (1) 𝒗=𝑎𝒊+𝑏𝒋 (2) 𝒗= <𝑎 , 𝑏>

Objectives Find the distance in space Find position vectors in space Perform operations on 3d vectors Find the dot product of 3d vectors Find the angle between two vectors

2-D Review What is the distance between points (5,6) and (2,-3) https://www.youtube.com/watch?v=KYcARiVEe1U

3D intro What is 3d?

3D Video http://www.youtube.com/watch?v=wfaiFcfoPfk http://www.youtube.com/watch?v=quoySiCVFfw

3D intro- Distance Plot points A – (2,1,3) B - (3,1,2) Draw a rectangular box and label points P and Q on opposite corners Make the length of the sides a,b,c What is the distance from P to Q?

Position vectors v starts at point (1,3,2) and end at point (3,6,-1) What is the position vector of v What is the magnitude of v What is 3v If w is <3,2,5> What is v+w 𝒗 . 𝒘 Angle between v and w

Summary These are the same formulas you had with other vectors, extended for an extra dimension (z-axis)

Homework Page 624 8-58 even