Question

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>

can you please explain step by step?

Answer 1

you are to find the Dot Product of \(v\) and \(w\)..

Answer 2

Just multiply the corresponding elements of the vector \(v\) and \(w\), and sum them..

Answer 3

\((3 \times -4) + (-8 \times -2) + (-3 \times -6) = ??\)

Answer 4

ohhh okay! haha thanks :)

Answer 5

If you come across any doubt, then let me know.. :)

Answer 6

okay thanks :)

Answer 7

do you know how to do this kind:

Let u = <-5, -9>, v = <6, 8>. Find -8u - 2v.
?

Answer 8

Firstly multiply -8 to all elements of \(u\)..

Answer 9

Then multiply \(-2\) with all elements of \(v\)..

Then simply add them..

Answer 10

40 + 72

-12 + (-16)

like that?

Answer 11

you can only add or subtract corresponding elements of the two vector.. First of one with first of second.. :)

Answer 12

See like this, I show you...

Answer 13

oh so

40 + (-12)
72 + (-16)

Answer 14

yep

Answer 15

But after adding, write result as <a,b>.. :)

Answer 16

ohhh okay!

Answer 17

Like : \(40 - 12 = 28\) and \(72-16 = 56\)

Then it will be : \(<28, 56>\)

Answer 18

thanks so much!!!

Answer 19

In vectors, always add corresponding elements of two or more vectors only..

Answer 20

gotcha

Answer 21

Yeah, keep it up, the more you practise, the more you will be gaining.. :)

Answer 22

thanks soooo much! that was really helpful, now I can do all of my problems :)

Answer 23

Good... :)