Question

Three vectors A, B, C in three-dimensional space satisfy the following properties

|| A || = || C || = 5,
|| B || = 1
|| A-B + C || = || A + B + C ||
If the angle formed by A and B is π / 8 find the one formed by B and C

Answer 1

`(7)/(8)\pi`

Explanation:

observe

||a–b+c|| = ||a+b+c||

(a-b+c)² = (a+b+c)²

(a+b+c)² – (a-b+c)² = 0

((a+b+c)+(a-b+c))((a+b+c)–(a-b+c)) = 0

(2a+2c)(2b) = 0

(a+c)b = 0

a•b + c•b = 0

||a||×||b||×cos(π/8) + ||c||×||b||×cos(θ) = 0

`\cos(\theta)=-(||a||* ||b|| * \cos((\pi)/(8)))/(||c||* ||b||)=-\cos((\pi)/(8))</p><p>\\ \theta=(7)/(8)\pi`