Answer:
[tex]\frac{7}{8}\pi[/tex]
Step-by-step 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
[tex]\cos(\theta)=-\frac{||a||\times ||b|| \times \cos(\frac{\pi}{8})}{||c||\times ||b||}=-\cos(\frac{\pi}{8})
\\ \theta=\frac{7}{8}\pi[/tex]
