three vectors A, B, C in three-dimensional space satisfy the following properties || A || = || C || = 5, || B || = 1 <

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

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Luna 1 week 2021-10-07T18:05:06+00:00 1 Answer 0

Answers ( )

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    2021-10-07T18:06:10+00:00

    Answer:

    \frac{7}{8}\pi

    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

    \cos(\theta)=-\frac{||a||\times ||b|| \times \cos(\frac{\pi}{8})}{||c||\times ||b||}=-\cos(\frac{\pi}{8})\\ \theta=\frac{7}{8}\pi

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45:7+7-4:2-5:5*4+35:2 =? ( )