Find the approximate angle between the vectors a 2 11 9 and

Find the approximate angle between the vectors a = (2, 11, -9) and b = (1, 3, 14). 38.6 degrees b. 116.2 degrees c. 155.5 degrees d. 90 degrees e. None of the above

Solution

Solution:

cos= a.b/|a||b|

given a=2i+11j-9k

b=1i+3j+14k

a.b=a_x · b_x + a_y · b_y + a_z · b_z

=(2)(1)+(11)(3)+(-9)(14)

=2+33-126

=-91

|a|=sqrt[2² +11² +(-9)^2]

  =sqrt(206)

|b|=sqrt[1² + 3² +14² ]

sqrt(206)

cos=-91/sqrt(206)sqrt(206)

=-91/sqrt(206²)

=-91/206

=cos^-1 (-91/206)

=116.2 Degrees

option(b)