Vector Operations (Scalar and Cross product)

Question 1

The dot product gives us what as a result

Answer 1

a scalar

Question 2

dot product formula

Answer 2

x_1y_1 + x_2y_2 + … + x_ny_n

Question 3

vector1 • vector1 is equal to

Answer 3

||vector_1||^2

Question 4

two vectors are orthogonal if

Answer 4

vector_x • vector_y = 0

Question 5

why is the zero vector orthogonal to every other vector

Answer 5

two vectors are orthogonal if their dot product is 0, so therefore any vector multiplied by the 0 vector will give 0, meaning all vectors are orthogonal to the zero vector

Question 6

is scalar(dot) product commutative?
ie does x • y = y • x

Answer 6

yes

Question 7

is scalar product distributive

ie does x • (ay + bx) = ax • y + bx • y

Answer 7

YES

Question 8

What is another name for the dot product

Answer 8

scalar product

Question 9

what is another name for the cross product

Answer 9

vector product

Question 10

what does the cross product result in

Answer 10

a vector

Question 11

the cross product can be used in a 2d plane true or false

Answer 11

FALSE

Question 12

formula for cross product

Answer 12

x_2y_3 - x_3y_2
x_3y_1 - x_1y_3
x_1y_2 - x_2y_1

Question 13

how do we find a vector which is perpendicular to two vectors

Answer 13

by finding their cross product

Question 14

how to find A, the angle between vector x and vector y

Answer 14

||x x y|| = ||x||•||y||•sinA

Question 15

x • (x x y)

y • (x x y)

Answer 15

both equal 0