Print your name: __________________________________________________ Worksheet on Vector Dot Products and Simple Matrix Mathematics 1. Given the vectors = {2, 5, 3} and b = {6, 9, 11}, what is the scalar result of the dot product a ? Show your work. 2. What are the norms (lengths) of vectors and from question 1? a b 3. What is the angle between vectors and from question 1? a b 4. What are the unit vectors and that coincide with vectors and from question 1? a b 5. What is the angle between vectors (from question 1) and (from question 4)? Show your a work. 6. Where (in terms of rows and columns) is the value located in a matrix c23 c? 7. Represent vector from question 1 as a 3x1 matrix where is the coordinate of a a a11 x Cartesian coordinate system, is the coordinate, and is the coordinate. a21 y a31 z 8. Represent vector from question 1 as a 1x3 matrix where is the coordinate of a b b11 x Cartesian coordinate system, is the coordinate, and is the coordinate. b12 y b13 z 9. If we define matrix as given below, (a) compute the product of the equation showing all c d , your work, and (b) what sort of mathematical object/entity might be considered to be? d 10. If we define matrix as given below, (a) compute the product of the equation showing all e p , your work, and (b) what sort of mathematical object/entity might be considered to be? p
Print your name: __________________________________________________ Worksheet on Vector Dot Products and Simple Matrix Mathematics 1. Given the vectors a = {2, 5, 3} and b = {6, 9, 11}, what is the scalar result of the dot product ? Show your work. 2. What are the norms (lengths) of vectors a and b from question 1? 3. What is the angle between vectors a and b from question 1? 4. What are the unit vectors and that coincide with vectors a and b from question 1? 5. What is the angle between vectors a (from question 1) and (from question 4)? Show your work. 6. Where (in terms of rows and columns) is the value c23 located in a matrix c? 7. Represent vector a from question 1 as a 3x1 matrix where a11 is the x coordinate of a Cartesian coordinate system, a21 is the y coordinate, and a31 is the z coordinate. 8. Represent vector b from question 1 as a 1x3 matrix where b11 is the x coordinate of a Cartesian coordinate system, b12 is the y coordinate, and b13 is the z coordinate. 9. If we define matrix c as given below, (a) compute the product d of the equation , showing all your work, and (b) what sort of mathematical object/entity might d be considered to be? 10. If we define matrix e as given below, (a) compute the product p of the equation , showing all your work, and (b) what sort of mathematical object/entity might p be considered to be?