If #A = <8 ,3 ,-7 >#, #B = <6 ,-4 ,5 >#, and #C=A-B#, what is the angle between A and C? Trigonometry Triangles and Vectors Vectors 1 Answer Dean R. May 6, 2018 #theta = arccos (121/sqrt(24034) ) approx 38.69^circ # Explanation: #A cdot C = |A||C| cos theta # # A = (8,3,-7)# #C= A-B=(8,3,-7)-(6,-4,5) = (2,7,-12)# # (8, 3, -7) cdot (2,7,-12) = |(8", "3", "-7)| \ |(2", "7 ", " -12)| \ cos theta# #cos theta = {8(2) + 3(7) + -7(-12)}/{\sqrt{ (8^2+3^2+7^2)(2^2+7^2+12^2) }} = 121/sqrt(24034) # #theta approx 38.69^circ # Answer link Related questions How do you write the components of vectors? How can vectors be represented? What does the i and j stand for in vectors? If #\vec{g}# is in standard position with terminal point (5, 5) and #\vec{h}# is in standard... If #\vec{i}# is in standard position with terminal point (1, 5) and #\vec{j}# is in standard... How do you find the coordinates of vector PQ in standard position given Points P( 4,5) and Q (-7,3)? Using (-3, -2) as the initial point, how do you draw the vector that represents the complex... Using (-3, -2) as the initial point, how do you draw the vector that represents the complex number #8#? How do you give the complex number form of the vector with the given initial and terminal point... How do you give the complex number form of the vector with the given initial and terminal point... See all questions in Vectors Impact of this question 427 views around the world You can reuse this answer Creative Commons License