Question

24.Two 6vectorsǐ arek givealuate the following-4ktand B=61-10İ +9k. Evaluate the following quantities (a) cos-'[A-B/AB] and (b) sin-i [A × BI /AB). (c) which give(s) the angle between the vectors?

Answer 1

here,

A = - 3 i + 7 j - 4 k

B = 6i - 10 j + 9 k

A.B = (- 3 i + 7 j - 4 k).( 6i - 10 j + 9 k)

A.B = ( -3 * 6 - 7 * 10 - 4 * 9)

A.B = - 124 units

|A| = sqrt(3^2 + 7^2 + 4^2) = 8.6 units

|B| = sqrt(6^2 + (-10)^2 + (9)^2) = 14.73 units

a)

arccos(A.B /(|A||B|)) = arccos(- 124/(8.6 * 14.73 )) = 168.2 degree

b)

A X B = (- 3 i + 7 j - 4 k) X ( 6i - 10 j + 9 k)

A X B = ( (-3) * (-10) k + (-3) * ( 9) (-j) + (7 ) * ( 6) * (-k) + 7 * 9 * i + (-4) * (6) * ( j) + (-4) * (-10) i)

A X B = (103 i + 3 j - 12 k)

arcsin(AXB /(|A||B|)) = arcsin((103 i + 3 j - 12 k) /(8.6 * 14.73))

c)

the answer to part(A) gives the angle between the vectors

so , the angle between vectors is 168.2 degree