Question

Find the value of b so that vectors U = 5i+12j and V = 4i+bj are perpendicular

Answer 1

when two vectors \(\vec v\) and \(\vec u\) are perpendicular, their dot product is zero

Answer 2

okk

Answer 3

hence just take the dot product and set it to zero\[\vec u\cdot\vec v=0\]and solve for \(b\)

Answer 4

Would the Dot product be 32 ?

Answer 5

I took 5x4 and 12x1 i don't know

Answer 6

the dot product can't be non-zero or else the two vectors would not be perpendicular, as I mentioned above.
why did you do 12x1 ?
the j-component of the second vector is our unknown, \(b\), not 1
try again keeping the variable \(b\) where it belongs

Answer 7

i got 20+12bj^2 is that ok ?

Answer 8

yes, but\[(\hat j)^2=\hat j\cdot\hat j=1\]so you can simplify that a bit
and what are we setting that expression equal to again?

Answer 9

b ?

Answer 10

no, two vectors are perpendicular if their dot product is...?

Answer 11

0

Answer 12

yes, so what are we solving?
write the whole equation please

Answer 13

ohhhhh i got it,

Answer 14

:)

Answer 15

0 = 20+12bj^2

Answer 16

-20/12

Answer 17

oh i see haha :))

Answer 18

yup :D
nice job!
(again j^2=1)

Answer 19

ohhh is it always like that ?

Answer 20

is j^2 always 1 you mean?

Answer 21

yes

Answer 22

yes, because \(\hat j=\langle0,1\rangle\), so \((\hat j)^2=\hat j\cdot\hat j=\langle0,1\rangle\cdot\langle0,1\rangle=1\)
(for the same reason, the \(\hat i\) disappeared)

Answer 23

ahh ok

Answer 24

thanks @TuringTest

Answer 25

anytime @Ala123 :D