8.2/8.4 Algebraic Vectors in 2-Space and 3-Space PDF

8.2,8.3.notebook January 03, 2018 8.2/8.4­ Algebraic Vectors in 2­space and 3­space objective: find the length of a vector and name a vector algebraically in 2 and 3 space. Write a vector as a linear combination of uni...

8.2,8.3.notebook January 03, 2018 8.2/8.4­ Algebraic Vectors in 2­space and 3­space objective: find the length of a vector and name a vector algebraically in 2 and 3 space. Write a vector as a linear combination of unit vectors 1 8.2,8.3.notebook January 03, 2018 2 8.2,8.3.notebook January 03, 2018 Unit Vector­ a vector that is parallel the x, y, or z axis and has a length of 1. i= (1,0)( this vector is in the direction of the positive x­axis j = (0,1)(this vector is in the direction of the positive y­ axis) In 3­space i = (1,0,0) j = (0,1,0) k=(0,0,1) A(2,­7), B(­1,5) Write AB as a sum of unit vectors. 3 8.2,8.3.notebook January 03, 2018 4 8.2,8.3.notebook January 03, 2018 Problems on the quiz: KNOW THESE! 1. While digging in the ground, Will pushes the shovel with a force of 630N and 70 degrees with the ground, What are the vertical and horizontal components, draw a picture. 2. 2 people kick a soccer ball at the exact same time. 1 with a force of 55N west and the other with a force of 70N south, what is the resulting force and direction of the soccer ball? 3. Find a unit vector in the same direction as vector V. v = (6,3) 4. Find the directed distance(ordered pair) of vector v if |V|= 15 and Θ= 125 degrees. 5. Determine if vector AB and vector CD are equivalent? A(3,5), B(6,9), C(­4,­4), D(­2,0) 6. Find a unit vector in the same direction as vector AB. A(8,12,7), B(2,­3,11). 7. Find the direction angle of the vector. ­5i + 9j 5