Question

Find the angle in degrees between the vectors a = (1,2,2) and b = (3,4,0). Approximate it to the nearest degree.

a. 43

b. 23

c. 33

d. 53

e. another answer

Answer 1

Given that two vectors a=(1,2,2) and b=(3,4,0)

if theta be the angle between two vectors a and b ,then we know that

a•b=|a|×|b| cos(theta) .............. (1)

now a=(1,2,2) and b=(3,4,0)

therefore |a|= sqrt(1^2+2^2+2^2)

=sqrt(1+4+4) = sqrt(9)=3

and |b|=sqrt(3^2+4^2+0^2)

=sqrt(9+16+0)=sqrt(25)=5

and. a•b = (1,2,2)•(3,4,0)

=1×3+2×4+2×0=11

hence from (1) using these we get

11=3×5 cos(theta)

or, cos(theta)=11/15=

or, theta = acos(11/15)

or, theta = 43° (approximately)

Hence the angle between two vector is 43°.