CK-12-Pre-Calculus Concepts

7.1. Basic Properties of Vectors http://www.ck12.org 3.A= ( 1 , 3 ),−→v=< 4 , 8 >,−→u =<− 1 ,− 5 > .A+−→v+−→u = ( 4 ...

http://www.ck12.org Chapter 7. Vectors 14.<− 5 , 10 > 15.< 6 ,− 8 > ...

7.2. Operations with Vectors http://www.ck12.org 7.2 Operations with Vectors Here you will add and subtract vectors with vectors ...

http://www.ck12.org Chapter 7. Vectors Scalar multiplicationmeans to multiply a vector by a number. This changes the magnitude o ...

7.2. Operations with Vectors http://www.ck12.org 92 = 12. 662 + 52 − 2 · 12. 66 · 5 ·cosθ θ= 34. 6 ◦ Example C Elaine started a ...

http://www.ck12.org Chapter 7. Vectors x^2 = 492 + 252 − 2 · 49 · 25 ·cos 135◦ x≈ 68. 98 N In order for Elaine to stay balanced, ...

7.2. Operations with Vectors http://www.ck12.org An airplane is flying at a bearing of 270◦at 400 mph. A wind is blowing due so ...

http://www.ck12.org Chapter 7. Vectors Determine the component form of 5−→v− 2 −→u. Determine the component form of− 2 −→v+ 4 − ...

7.3. Resolution of Vectors into Components http://www.ck12.org 7.3 Resolution of Vectors into Components Here you will find unit ...

http://www.ck12.org Chapter 7. Vectors There are two standard unit vectors that make up all other vectors in the coordinate plan ...

7.3. Resolution of Vectors into Components http://www.ck12.org ( 305 √ 3 2 ) 2 + ( 395 2 ) 2 =c^2 329. 8 ≈c The airplane is trav ...

http://www.ck12.org Chapter 7. Vectors −→L+CON−−→+−−→CY N+−→T =< 0 , 0 > < 8 ·cos 41◦, 8 ·sin 41◦>+< 10 ·cos 100◦ ...

7.3. Resolution of Vectors into Components http://www.ck12.org The vector−→BPis<− 7 , 13 >. First take the unit vector an ...

http://www.ck12.org Chapter 7. Vectors 7.4 Dot Product and Angle Between Two Vec- tors Here you will compute the dot product bet ...

7.4. Dot Product and Angle Between Two Vectors http://www.ck12.org Notice how vectors going in generally the same direction have ...

http://www.ck12.org Chapter 7. Vectors u·v=<u 1 ,u 2 >·<v 1 ,v 2 > =u 1 v 1 +u 2 v 2 =v 1 u 1 +v 2 u 2 =<v 1 ,v 2 ...

7.4. Dot Product and Angle Between Two Vectors http://www.ck12.org The dot product between the two vectors<− 1 , 1 >and< ...

http://www.ck12.org Chapter 7. Vectors u·v |u||v|=cosθ < 3 ,√ 5 >·< 2 , 8 > 34 ·√ 68 =cosθ √^6 +^35 34 ·√ 68 =cosθ c ...

7.5. Vector Projection http://www.ck12.org 7.5 Vector Projection Here you will project one vector onto another and apply this te ...

http://www.ck12.org Chapter 7. Vectors The definition of vector projection for the indicated red vector is the calledpro juv. Wh ...