r Salman In Our Hearts l 11 phys252HW01pdf Phys252 HWork 1

.:, r Salman In Our Hearts l 11. phys-252-H.W-01.pdf Phys252> H.Work # 1 PHYS252 1439-6-17·29 O) Given three vectors as following: 21+3)-k . 4) a Which of vectors in one dimension, or two dimensions, or three b) Find the angle between the veclors A and B c)A+ Calculate Find a unit n of the vector that is perpendicular to both vectors A and B e Find the angle that vector A makes with y axis Find the angle that vector A makes with z axis g) Calculate: A.(EnQ

Solution

A = 2i + 3j - k => |A| = sqrt(4 + 9 + 1) = sqrt(14)

B = 4i - j + 2k => |B| = sqrt(16 + 1 + 4) = sqrt(21)

C = 4j => |C| = 4

a) C = 1 dimension, A & B are of 3 dimensions

b) angle between A and B = cos^-1(A.B/(|A||B|) = cos^-1((8 -3 -2)/sqrt(21x14)) = 79.92^o  

c) R = 6i + 2j + k => |R| = sqrt(36 + 4 + 1) = sqrt(41) = 6.403

d) n = (AXB)/|AXB| = (5i - 8j -14k)/sqrt(25 + 64 + 196) = (5i - 8j - 14k)/sqrt(285)

e) angle = cos^-1(3/sqrt(14)) = 36.699^o

f) angle = cos^-1(-1/sqrt(14)) = 105.5^o or (180 - 105.5 = 74.5^o)

g) A.(BXC) = (2i + 3j - k).((4i - j + 2k)X(4j)) = (2i + 3j - k).(16k - 8i) = -16 -16 = -32