Find the angle 𝜃 (in radians) between the vectors. (Round your answer to two decimal places.)

Question

u = 3i + 4j

v = -9i + 5j

Answer 1

about 90+ degrees, pi/2+

graph the vectors.

visually they look slightly more than 90 degrees

use the dot product: -9(3)+5(4) = -27+20=-7

divide by the product of the vectors' magnitudes

-7/5sqr106

then take the inverse cosine

= 97.82 degrees

= 1.71 radians

= 0.54 pi radians

or use the law of cosines with sides = 5, sqr106 and sqr145

find the angle opposite sqr145