Transcription of Vectors Summary - a-levelmaths.com
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Vectors Summary - a-levelmaths.com
Vectors Summary 1. Scalar product (dot product): cos||||baba= Laws of dot product: (i) abba = (ii) acabcabacba + = + =+ )( (iii) 2||aaa= (angle between two identical Vectors is 0 degrees) (iv)aba = 0 and b are perpendicular Applications: (i) Projection vector: Length of projection L= | ADAB| B Projection vector AC = ( ADAB) AD Foot of perpendicular = OC =OA+AC Shortest distance from B to line A C D =2||BC=22||LAB [OR = | ADAB| ] L (ii) Acute angle between two lines.
7. Shortest distance from plane to origin: For a plane with equation r•n=k, the shortest distance from the plane to the origin is given by |n| k. 8. Distance between 2 planes: For 2 planes with equations r•n=k 1
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