Cross Product

Question 1

Cross Product Theorem

Answer 1

given 2 vectors a and b, the cross product of the two will give you a vector that perpendicular to the two

Question 2

what a x b equals

Answer 2

the positive vector c; -b x a

Question 3

what b x a equals

Answer 3

the positive vector d or the negative vector c (d=-c)

Question 4

length or magnitude of a x b

Answer 4

|a x b| = |a| |b| sin (theta)

Question 5

what i x j equals

Answer 5

the positive vector k

Question 6

what j x k equals

Answer 6

the positive vector i

Question 7

what k x i equals

Answer 7

the positive vector j

Question 8

what the vector -k is in cross product form

Answer 8

j x i

Question 9

what the vector -i is in cross product form

Answer 9

k x j

Question 10

what the vector -j is in cross product form

Answer 10

i x k

Question 11

how to figure out if the vector product of a cross product will be positive

Answer 11

go from left to right on the vector, if they make an upside down v it will be psotive (right hand rule)

Question 12

cross product equation

Answer 12

a x b = | i j k | = i (a2b3-b2a3) - j (a1b3 -
|a1 a2 a3 | b1a3) + k (a1b2-a2b1)
|b1 b2 b3 |

Question 13

area of a parallelogram (|axb|)

Answer 13

|axb|= bh= |a|h=|a||b|sin (theta)

Question 14

how to combine 3 points to 2 vectors (P, Q, R)

Answer 14

subtract terminal end from intial end, and the same for the other (makes 2 vectors) ; PQ=Q-R and PR=R-P

Question 15

how to find perpendicular plane

Answer 15

cross product of two vectors

Question 16

volume of a parallelepiped without theta

Answer 16

base times height (base= area of parallelepiped); ( a x b) * c

Question 17

area of parallelepiped

Answer 17

|a||b|sin(theta) = |a x b|

Question 18

height of parallelepiped

Answer 18

|c|cos (theta)

Question 19

volume of a parallelepiped with theta

Answer 19

|a x b| |c| cos (theta)