Question

If `A = <5 ,4 ,3 >`, `B = <2 ,-7 ,6 >` and `C=A-B`, what is the angle between A and C?

Answer 1

0.929 radians `≈ 53.2^@`

Explanation:

To calculate the angle between 2 vectors `ula " and" ulc`
Use the following formula.

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

here C = A - B = (5,4,3) - (2,-7,6) = (3,11,-3)

now `ula . ulc = (5,4,3) . (3,11,-3)`

`= (5xx3) + (4xx11) +(3xx-3) = 15 +44 -9 = 50`

`|ula| = sqrt(5^2+4^2+3^2) = sqrt(25+16+9) = sqrt50`

and `|ulc| = sqrt(3^2+11^2+(-3)^2) = sqrt(9+121+9) =sqrt139`

`rArr theta = cos^-1(50/(sqrt50xxsqrt139)) ≈ 0.929 " radians"`