Angle in Radians between two vectors

Question

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

u	=	3i − j
v	=	15i − 5j

My TI84 calculator keeps giving me errors... can anyone help me solve this problem? I have done the work but according to my book (based on other examples) its not the correct answer...

Answer 1

v = 3u, therefore the two vectors are parallel.

Answer 2

I would like to see what you did. It is very likely that you merely left out some parentheses or didn't hit the "equals" key at the right step.

However,

Numerator: (3)(15) + (-1)(-5) = 50.

Denominator: SQRT(3^2+(-1)^2)SQRT(15^2+(-5)^2) = SQRT(10)SQRT(250) = SQRT(2500) = 50

Wow, that means the ratio is 1.

cos^-1(1) = 0

Answer should be zero radians; the vectors are parallel.

I suspect that you may perhaps have tried to square a negative number without putting it in parentheses.