Question

Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

Answer 1

Is that supposed to be:
Find a - b.
a = 7i - 4j
b = 4k + 3j

Answer 2

not that i know of, i copied and pasted it right from my worksheet, so idk

Answer 3

* b = 4i + 3j

Answer 4

This is Pre-Calculus. Am I correct?

Answer 5

oh yes, i thought you meant to put a k. but yes this is.

Answer 6

These are just 2 dimensional vectors, of the form "i" and "j". So, you are going to have to use (xa-xb), (ya-yb).

Answer 7

so would the answer be 16?

Answer 8

So, tell me. What would go into (xa-xb), (ya-yb) from these equations:
a = 7i - 4j
b = 4i + 3j

Answer 9

(7i-4i)
(-4j-3j)

Answer 10

Correct now solve them.

Answer 11

3i, -7j

Answer 12

Correct. Good job :)

Answer 13

Or if you wanted to leave it in coordinates, it would be (3, -7).

Answer 14

<28, -12>

16

-40

<11, -1>

Answer 15

but those are the answers possible, so what now? ):

Answer 16

can you show me how you did it? or would that take too long?

Answer 17

did you just multiply each of the vectors?

Answer 18

Correct, You said you got 16 before?

Answer 19

yes,

Answer 20

Okay, actually I think you made a typo which messed me up. Is it a+b?

Answer 21

Because if we solve it any other way we are always going to come out with <3, -7> which is not correct. If the question is a+b then the last choice <11, -1> would have been correct.

Answer 22

hen i look at it in the other window, it looks like a minus sign, but when i copied it, it looks like a multiplication dot thingy

Answer 23

a = 7i - 4j, b = 4i + 3j
he is asking for a multiplication then as we know that i and j are perpendicular to each other and their product becomes zero, ie
i*j = 0 and i*i = 1 and j*j =1 as i and j are unit vectors now
a*b = (7*4)(i*i) + (7*3)(i*j) + (-4*4)(j*i) + (-4*3)(j*j)
a*b = 28 + 0 +0 =12
a*b = 28-12
a*b = 16

Answer 24

so 16 would be the final answer??

Answer 25

when we multiply ( scalar multiplication i mean just normal multiplication) two unit vectors then vector form vanishes

yes, 16 is the final answer

Answer 26

Finally! Whoo *dances in circle*. Ahem! Anyways, I'm sorry for the mistake, thanks @SandeepReddy ;)

Answer 27

@ecociuba, \(a\cdot b\) is the dot product of \(a\) and \(b\).

If \(a,b\in\mathbb{R}^n\) (meaning \(a=(a_1,a_2,...,a_n)\)), then
\[a\cdot b=\sum_{k=1}^na_kb_k\]

Answer 28

its ok, im just glad i got the answer right in the first place :p

Answer 29

No problem e.cociuba :)

Answer 30

thank you both so much! i wish i could give out 2 medals

Answer 31

or we can just by heart form @SithsAndGiggles gave you.
just multiplying corresponding numbers of unit vectors in this case i and j

Answer 32

Thanks @SithsAndGiggles :) As you can see, my skills in pre-calc are a bit rusty. Anyways, sorry for the mistakes done and thanks for the corrections all :)