Graph the vectors.

Question

u = 2i - 4j

v = 9i + 3j

Top Left: A, Top Right: B, Bottom Left: C, Bottom Right: D

Find the degree measure of the angle 𝜃 between the vectors. (Round your answer to two decimal places.)

𝜃 = ______°

Answer 1

u = 2i - 4j is the "unit-vector representation" of the vector <2,-4> that is 2 units to the right, and 4 units downwards.

v = 9i + 3j is that of the vector <9,3> that is 9 units to the right, 3 units upwards.

Hence the answer is A.

Answer 2

u = 2i - 4j

v = 9i + 3j

If you need to find an angle between two vectors use Dot product

u . v = Ιl u ll ll v ll cos θ

cos θ = u . v / Ιl u ll ll v ll

u . v = 2*9 - 4*3 = 18-12 = 6

Ιl u ll = √ ( 2² + 4^{2 )} = √ 4+ 16 = √ 20 = 2 √5

Ιl v ll = √ ( 9² + 3^{2 )} = √ 81+ 9 = √ 90 = 3 √10

cos θ = 6 /( 2 √5 3 √10) = 1/ √50

θ = cos ^-1 1/ √50

Answer 3

u ends at (2, -4)

v ends at (9, 3)