Linear Motion: Basic Vector Operations


This note provides an introduction to calculations involving vectors. It covers adding and resolving vectors, both co-linear and perpendicular. This is ideal preparation for calculations that will be encountered in the Leaving Certificate examination.
Note by alex.examtime9373, updated more than 1 year ago
Created by alex.examtime9373 almost 10 years ago

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Adding Co-linear Vectors AKA finding a resultant Vectors are co-linear when their directions are parallel

Adding vectors that act in the same direction --> add magnitudes, use same direction Adding vectors that act in opposite directions --> subtract magnitudes, use direction of larger vector

Adding Perpendicular Vectors

Use Basic Trigonometry: Pythagoras' Theorem Trigonometric functions: sine, cosine, tangent

Pythagoras' TheoremThe square of the hypotenuse is equal to the sum of the squares of the other two sides

Trigonometric Functions Sine Cosine Tangent Useful mnemonic: Silly Old Harry Caught A Herring Trawling Off America

Triangle Law for Perpendicular Vectors: The resultant of any two perpendicular vectors is equal to the hypotenuse of the right-angled triangle formed by the two vectors placed "tip to tail" The second vector starts at the end of the first vector Use Pythagoras' Theorem to get the magnitude of the resultant vector Use trigonometric functions to get the direction of the resultant vector The diagram shows the addition of vectors AB and BC. The resultant vector is AC

Resolving Vectors This is the opposite of finding the resultant A vector is resolved into two component perpendicular vectors The component vectors are equal to the magnitude of the original vector multiplied by sin θ  and cos θ 

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