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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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