Dot Product Properties

Question 1

a * a =

Answer 1

|a|^2

Question 2

a * b=

Answer 2

|a||b| cos (x)

Question 3

The dot product of perpendicular vectors

Answer 3

a * b = 0

Question 4

(a + b) *c =

Answer 4

a c + b c

Question 5

a * (b+c) =

Answer 5

a * b + a * c

Question 6

|a * b|

Answer 6

<= |a||b|

Question 7

|a + b|

Answer 7

<= |a||b|

Question 8

|a +b|^2=

Answer 8

|a|^2 + |b|^2 + 2a *b

Question 9

|a - b|^2=

Answer 9

|a|^2 + |b|^2 - 2a *b

Question 10

|a +b|^2 + |a - b|^2=

Answer 10

2|a|^2 + 2|b|^2