Question

if vector A=5i, B sub z=0, absolute value of vector B=7, vector A x vector B=2.5k, find vector B

Answer 1

\[
\mathbf A=5\mathbf{i}+0\mathbf{j}+0\mathbf k
\]

Answer 2

\[
\mathbf B=b_x\mathbf{i}+b_y\mathbf{j}+0\mathbf k
\]

Answer 3

First do the cross product.

Answer 4

but what pouts do i use for bi and bj

Answer 5

Keep them as variables \(B_x\) and \(B_y\)

Answer 6

i got o,o,5By

Answer 7

Notice how: \[
5B_y=2.5
\]

Answer 8

Now you can find \(B_y\)

Answer 9

you lost me, the 2.5 comes from b=k right?

Answer 10

vector A x vector B=2.5k

Answer 11

\[
\mathbf A\times \mathbf B =2.5\mathbf k
\]

Answer 12

\[
2.5\mathbf k = 5B_y\mathbf k
\]

Answer 13

ok that was given...

Answer 14

so By=.5?

Answer 15

Yes.

Answer 16

Now: \[
\sqrt{B_x^2+B_y^2+0^2}=7
\]

Answer 17

Because \[
\|\mathbf B\|=7
\]

Answer 18

So \[
B_x^2+B_y^2=7^2
\]

Answer 19

this is to find Bx?

Answer 20

Yes.

Answer 21

which I'm getting = 48.25

Answer 22

Bx sqaured+.5^2=49
Bx=48.75?

Answer 23

You need to do the square root.

Answer 24

so im getting final answer of 6.98212i+.5j
correct?

Answer 25

thank you, i learned a different approach

Answer 26

\[
|B_x|=\frac{\sqrt{195}}{2}
\]

Answer 27

There are two answers...

Answer 28

\[
B_x=\pm \frac{\sqrt{195}}{2}
\]

Answer 29

i see, from the square root

Answer 30

A different approach? There is only one approach I can think of. anyway we have the answer. there are two.

Answer 31

I'm fairly new at this material

Answer 32

Do you understand the work we did? Do you understand why there are two answers?

Answer 33

yes, 2 answers because anytime you square root, you have plus answer and minus answer, and the work we did was, the way i see it, filling in the gaps from the info we got to complete to formula to find the answer