Question

I need help with one more question. My textbook doesn't exactly explain how to do this problem.
"Find the angle between the vectors u and v if u = - 4j + 3j and v = 3i + 2j. Round answer to two decimal places." My main confusion is what I do with the i's and j's.

Answer 1

the i's and j's label the coordinates.
you can use "tuple" notation <-4, 3> dot <3,2>
or i,j notation. they mean the same thing.

Answer 2

there are two ways to calculate the dot product.
the first way is
<a,b> dot <c,d> = ac + bd (multiply "corresponding" components, and add the products)

the other way:
v dot u = |v| |u | cos A
where |u| mean the "length" (computed as sqr( |u|^2)
and A is the angle between the two vectors

Answer 3

Ok, i'll be back with an answer.

Answer 4

for this problem you use both ways.

use the multiply corresponding elements and add to find the number for the dot product.
also find the length of both of your vectors.
then you use the 2nd way to "solve for cos A"

cos A = (u dot v)/ (|u| |v| )

Answer 5

Once I have the lower values do I multiply them? btw this is what I have:\[\frac{ -6 }{( 5)(3.60) }\]

Answer 6

yes, in exact terms you have
\[ \cos A = \frac{-6}{5 \sqrt{13}} \]
now "take the inverse cosine" of both sides to find the angle A between the two vectors:
\[ A = \cos^{-1} \left( \frac{-6}{5 \sqrt{13}} \right) \]
you will need a calculator to find this value

Answer 7

Here is a plot using geogebra

Answer 8

1.91 Thanks for all the help and patience!