Question

What is the angle between `<-4,3,-8 >` and `< 6,-3,8 >`?

Answer 1

Angle between `< -4,3,-8>` and `< 6,-3,8>` is `170.01^o`

Explanation:

Angle between two vectors `vecu=a_1hati+b_1hatj+c_1hatk` or `< a_1,b_1,c_1>`

and `vecv=a_2hati+b_2hatj+c_2hatk` or `< a_2,b_2,c_2>` is given by

`costheta=((vecu*vecv))/((|vecu|*|vecv|))`,

where `vecu*vecv=a_1a_2+b_1b_2+c_1c_2`

and `|vecu|` or `|vecv|` are magnitudes of vectors `vecu` or `vecv` and here they are

`sqrt(a_1^2+b_1^2+c_1^2)` and `sqrt(a_2^2+b_2^2+c_2^2)`

Hence angle between `< -4,3,-8>` and `< 6,-3,8>` is given by

`costheta=((-4)xx6+3xx(-3)+(-8)xx8)/(sqrt((-4)^2+3^2+(-8)^2)xxsqrt(6^2+(-3)^2+8^2))`

= `(-24-9-64)/(sqrt(16+9+64)xxsqrt(36+9+64))`

= `-97/(sqrt89xxsqrt109)`

= `-97/(9.43398xx10.44031)`

= `-0.9848`

and `theta=170.01^o`