What would I need to do to approximate the angle between the two vectors 4i-3j and 4i+3j.
we will use the formula for the dot product, i hope you know what the dot product is:
we have:
cos(x) = a*b/(|a||b|)
where * means dot product and x is the angle between the two (nonzero) vectors:
a*b = <4,-3>*<4,3> = 4*4 + (-3)*3 = 16 - 9 = 7
|a| = sqrt(4^2 + (-3)^2) = sqrt(25) = 5
|b| = sqrt(4^2 + 3^2) = sqrt(25) = 5
=> cos(x) = 7/(5)(5) = 7/25
=> x = cos^-1(7/25)
=> x = 1.287 radians
or x = 73.74 degrees
Hello, gretchen,
1. draw a sketch (see attachment).
2. both vectors have the same length (l = 5) thus you deal with the legs of an isosceles triangle.
3. use half of the isosceles triangle: It is a right triangle.
4. now you can calculate the angle by:
2*arctan(3/4) = 73.74°
EB