Magnitude The magnitude of a vector is represented

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Magnitude • The magnitude of a vector is represented by its length. • You

Magnitude • The magnitude of a vector is represented by its length. • You can multiply the magnitude of a vector by a scalar quantity to change its length. A = 10 m 2 A =20 m 0. 5 A =5 m

Direction • All vectors must have a direction. – North, south, east, west –

Direction • All vectors must have a direction. – North, south, east, west – Or an angle • Sometimes measured from the horizontal or vertical • Sometimes measured from the positive x-axis and around to 360 o 7 m =1 C 40 o 30 o C= B= m 15 20 m 230 o

‘Adding’ Vectors A = 10 m 40 o • Resultant points from start to

‘Adding’ Vectors A = 10 m 40 o • Resultant points from start to finish. 20 B C= m 5 =1 m • Must manipulate all vectors so they are put “tip to tail” 30 o

Sketch the vector sum of A+B • Must manipulate all vectors so they are

Sketch the vector sum of A+B • Must manipulate all vectors so they are put “tip to tail” • Resultant points from start to finish. m B 40 o A = 10 m 5 =1

Sketch the vector sum of A+B+C A = 10 m B 40 o C=

Sketch the vector sum of A+B+C A = 10 m B 40 o C= m 5 =1 20 m • Must manipulate all vectors so they are put “tip to tail” • Resultant points from start to finish. 30 o

Sketch the resultant of A-B • Flip the direction of the one being subtracted

Sketch the resultant of A-B • Flip the direction of the one being subtracted • Then put tip to tail and follow adding procedure A = 10 m m B 40 o 5 =1

Components of Vectors • Every vector will have a… – Horizontal component that points

Components of Vectors • Every vector will have a… – Horizontal component that points directly left or right – Vertical component that points directly up or down. 5 m ve l a igin = 2 r cto Or Horizontal component Vertical component • The components should be drawn tip to tail and lead to the same point as the original vector. • The angle goes by the start.

Calculating Vector Components 5 m ve l a igin = 2 r cto Or

Calculating Vector Components 5 m ve l a igin = 2 r cto Or Horizontal component Vertical component •

Find the components of the following vectors m m 20 A = 10 m

Find the components of the following vectors m m 20 A = 10 m C= B 5 =1 40 o 30 o

Find the magnitude and direction of A+B • Step 1: find the components of

Find the magnitude and direction of A+B • Step 1: find the components of each vector • Step 2: add all of the x-components together to find the resultant’s xcomponent • Step 3: add all of the y-components together to find the resultant’s ycomponent • Step 4: build your actual resultant out of its components you just fund. • Step 5: use Pythagorean Theorem and Soh. Cah. Toa to find magnitude and direction of resultant. A = 10 m m B 5 =1 40 o RESULTANT X-component: 10 m+11. 5 m = 21. 5 m Y- component: 0 m+9. 6 m = 9. 6 m