Question

If `A = <4 ,2 ,-5 >`, `B = <6 ,4 ,9 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`2.91" radians" , ( 166.8^@)`

Explanation:

To calculate the angle between 2 vectors `ula" and" ulc`

use: `costheta =( ula . ulc)/(|ula||ulc|)`

where `theta" is the angle between" ulaand" ulc`

here C = A - B = (4,2,-5) - (6,4,9) = (-2,-2,4)

hence: `ula . ulc = (4,2,-5) . (-2,-2,4)`

`= (4xx-2)+(2xx-2) +(-5xx4) = -8-4-20 = -32`

`|ula| = sqrt(4^2+2^2+(-5)^2) = sqrt(16+4+25) = sqrt45`

and`|ulc| = sqrt((-2)^2+(-2)^2+4^2) = sqrt(4+4+16) = sqrt24`

`rArr theta = cos^-1((-32)/(sqrt45xxsqrt24)) ≈ 2.91" radians"`