Question

find the degree measure of the angle between the vectors. u= 2i-3j v=4i+3j

Answer 1

use the dot product to evaluate the angle between them.

Answer 2

\[ \large \vec{a} \cdot \vec{b} = ab \cos\gamma \]
where gamma is the angle you want to measure between them.

Answer 3

but what do I do with i and j? do i include them in the formula?

Answer 4

no no, i and j are only unit vectors, you know what they mean?

Answer 5

\[\tan^{-1} (j/i)\] will give you the angle of the vector.

Answer 6

I'm a little confused on what unit vectors are.

Answer 7

@Ellyxart, unit vectors are vectors of length 1 (unit length) that point (in the normal case) towards their respective axis, so i points into the direction of the x-axis, j points in the direction of the y-axis, and k would point in the direction of the z-axis.

So when you have a notation like 2i, that only means 2 units into the direction of the x-axis.

Answer 8

Oh that makes perfect sense! thank you so much!

Answer 9

you are welcome.