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 Algebra Pre-Algebra and Basic Algebra Math Forum

 March 11th, 2018, 09:30 PM #1 Senior Member   Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry [ASK] About Vector and Angle Given w = |v|âˆ™ u + |u| âˆ™ v. If Î¸ = âˆ (u âˆ™ w) and Ï† = âˆ (v âˆ™ w) then â€¦. a. Î¦ â€“ Î¸ = 90Â° b. Î¸ + Ï†= 90Â° c. Î¸ = Ï† d. Î¸ â€“ Ï† = 90Â° e. Î¸ â€“ Ï† = 180Â° What I have done: $\displaystyle \cos\theta=\frac{u\cdot w}{|u||w|}$ and $\displaystyle \cos\phi=\frac{v\cdot w}{|v||w|}$ Then I substituted them as |v| and |u| to the given equation and got: $\displaystyle w=\frac{v\cdot w}{|w|\cos\phi}\cdot u+\frac{u\cdot w}{|w|\cos\theta}\cdot v$ What to do after this? I am stuck. Last edited by skipjack; March 12th, 2018 at 01:26 AM. March 12th, 2018, 07:30 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,384 Thanks: 2011 Let $u = |u|\hat{u}$ and $v = |v|\hat{v}$, then $w = |u||v|(\hat{u} + \hat{v})$ and $|w| = |u||v||\hat{u} + \hat{v}|$. $\displaystyle \cos(\theta) = \frac{u\cdot w}{|u||w|} = \frac{|u|^2|v| + |u|^2|v|(\hat{u}\cdot\hat{v})}{|u|^2|v||\hat{u} + \hat{v}|}= \frac{1 + \hat{u}\cdot\hat{v}}{|\hat{u} + \hat{v}|} = \cos(\varphi)$ Thanks from topsquark and AKM17Pro Tags angle, vector Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post noobinmath Calculus 4 March 6th, 2016 12:06 PM Tangeton Trigonometry 4 January 9th, 2015 03:13 AM M0ns7erS0u1 Linear Algebra 1 September 19th, 2013 12:41 PM yogazen2013 Algebra 2 August 12th, 2013 01:51 AM renoald Linear Algebra 3 October 31st, 2011 08:13 AM

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