Question

When a question asks to use vectors v=3i+j-k and w=-3i+2j-k to find an equation v*w do i just plug in and multiply?
so it would just be
(3i+j-2k)*-3i+2j-k

and then how would i solve that?

Answer 1

Do you mean the dot product of the two vectors?

Answer 2

yes, the multiplication would be the so-called 'dot product'

Answer 3

the question says "use the vectors v=3i+j-k and w=-3i+2j-k to find the expression.

then there are 2 questions based off of that, one of which is v*w, the other is -v+2w

Answer 4

hmm

Answer 5

then is not the dot product

Answer 6

in this case, you'd do it just like you'd any other expression with variables

(3i+j-k)(-3i+2j-k)

Answer 7

thats what i thought, then i would just leave the variables as variables?

Answer 8

yes

Answer 9

they aint variables, they are "markers"

Answer 10

the only major thing that happens, is the 'i' may turn into a \(i^2\) thus becoming "-1", is about it, and then add and cancel factors accordingly

Answer 11

ok cool, thanks for your help

Answer 12

(x,y,z) --> (xi + yj + zk)

Answer 13

addition, is the same procedure, just like you'd any other expression, and the result will be a complex expression

Answer 14

cool, thanks again

Answer 15

That is the dot product.

\[\Large \vec a \cdot \vec b = a_{x}*b_{x}+a_{y}*b_{y}+a_{z}*b_{z}\]

Answer 16

'i' means in the direction (parallel to) of the x-axis, 'j' means in the direction of the y-axis, and 'k' means in the direction of the z-axis.

\[\Large \vec a = 2 \hat i+3 \hat j+1 \hat k = <2,3,1>\] would be graphed