Question

Determine which of the given vectors are not orthogonal:
a. u = 3i, v = 8i + 7j
b. u = 3j, v = 7i
c. u = 3i, v = 7j
d. u = 3i – 8j, v = 8i + 3j

Answer 1

the dot product of orthogonal vectors equals zero

Answer 2

do they all equal zero?

Answer 3

only the orthogonal pairs of vectors will have a zero dot product

Answer 4

what do you get for the dot product of the first pair?

u = 3i, v = 8i + 7j

u⋅v =

Answer 5

77

Answer 6

no wait i got 31

Answer 7

to compute the dot product of vectors,
simply add the products of corresponding components

x = x_1i + x_2j
y = y_1i + y_2j

x⋅y = x_1y_1 + x_2y_2

Answer 8

was I wrong?

Answer 9

u = 3i v = 8i + 7j
= 3i+0j

u⋅v = 3*8 + 0*7 =

Answer 10

ohhhhhhhhhhhhh i didnt add the 0s...

Answer 11

the only one not is a!!!

Answer 12

right?

Answer 13

that is true but what is a.'s dot product equal to ?

Answer 14

31

Answer 15

u⋅v = 3*8 + 0*7 =

Answer 16

ohhhhh 24

Answer 17

got it

Answer 18

yeah 24

Answer 19

THANK YOU

Answer 20

now b.

u = 3j, v = 7i

u⋅v =

Answer 21

0

Answer 22

right because 0*3+7*0=0

Answer 23

c. u = 3i, v = 7j

is the almost the same as b.

Answer 24

d.

u = 3i – 8j, v = 8i + 3j

u⋅v = .. .. ..