PHY 107 1st Edition Lecture 3 Outline of Last Lecture I. Significant FiguresII. Vectors- Unit VectorsIII. Adding and subtracting vectorsOutline of Current Lecture IV. Multiplying vectors- Dot product- Cross productCurrent LectureMultiplying Vectors:- Multiplying a vector by a scalar´b=s ´a (where s is a number) → find the components of vector ´aand multiply each by s to generate the components of vector ´b The magnitude of ´b is equal to s times the magnitude of ´a → b = |s|a- If s > 0, vector ´b has the same direction as ´a, if s < 0 then vector ´b has the opposite direction- Dot product of two vectors (scalar product) : ´a · ´b´a · ´b = abcosθ (if you are given the angle between the vectors)´a · ´b = axbx + ayby + azbz (by components) - Cross product of two vectors (vector product) : ´a x ´b = ´c Magnitude of resultant vector, ´c, is c = absinθ Direction of ´c is perpendicular to the plane, P, defined by the vectors ´a and ´b Sense of ´c is given by the right hand rule- Place the vectors ´a and ´b tail to tail- Rotate ´a in the plane P along the shortest angle so that it coincides with´b- Rotate the fingers of the right hand in the same direction- Thumb of the right hand gives the sense of ´c Calculating with components:These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.-´a = ax´i + ay´j + az´k, ´b = bx´i + by´j + bz´k, ´c = cx´i + cy´j + cz´k- cx = aybz – azby cy = azbx – axbz cz = axby - aybx Order IS important in cross product-´b x ´a = – (´a x
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