Find the angle 𝜃 (in radians) between the vectors. (Round your answer to two decimal places.) u = −3i − 2j v = −8i + 9j

Answer 1

If θ is the angle between your two vectors, then you can you can find this angle by finding cosine of θ first.

cos θ is equal to the ratio between dot product of the vectors and product of magnitudes of the vectors.

Dot product of you vectors is equal to (-3)(-8)+(-2)(9)=6

Magnitude of your first vector is square root of (-3)^2+(-2)^2 which is square root of 13.

Magnitude of second vector is square root of (-8)^2+9^2 which is square root of 145.

If you put all these together you have that cos θ= 6/(sqrt(13) sqrt(145)).

You can do the math now, use your calculator and inverse of cosine to find your angle.

Hope it helps

Answer 2

Find the angle 𝜃 (in radians) between the vectors. (Round your answer to two decimal places.) u = −3i − 2j v = −8i + 9j

For finding angle between two vectors we use dot product rule (.)

A . B = !A! !B! Cos theta

So Cos theta = A.B/ !a! *!B!

A. B = U. V = ( -3i -2j). (-8i +9j) and !A! = sqrt ( 9+4 ) = sqrt (13) a d !B! = sqrt ( 64 + 81) = sqrt ( 145)

Cos theta = (24 -18) / sqrt 13* sqrt 145 = 6/sqrt ( 1885)= 6/43.412 =0.14

Theta = Cos-1 ( 0.14) = arcCos (0.14) =1.43 radian