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 October 11th, 2018, 10:15 PM #1 Member   Joined: Oct 2012 Posts: 78 Thanks: 0 Find a vector? Let u , v a vectors of 2-dim such that u=<4,-2> ,|v|=10 the angle between u and v is 45 degree. Find a coordinate for v satisfies these conditions. October 12th, 2018, 08:58 AM   #2
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$\cos(45^\circ) = \dfrac{\vec{u} \cdot \vec{v}}{|\vec{u}|\cdot|\vec{v}|}$

$\vec{u} = <4,-2>$, let $\vec{v} = <a,b>$

$\dfrac{1}{\sqrt{2}} = \dfrac{4a + (- 2)b}{\sqrt{20} \cdot 10} \implies 4a-2b = 10\sqrt{10}$

also, $a^2+b^2=100$

Quote:
 Find a coordinate for v satisfies these conditions.
can solve the system of equations to finish? October 13th, 2018, 05:35 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 The points (0, 0), (4, -2), (6, 2), and (2, 4) are the vertices of a square whose diagonals have length 2√10. Hence the desired vector is (1/2)<6, 2> or (1/2)<2, -6>, i.e. <3, 1>, or <1, -3>. October 13th, 2018, 06:50 AM   #4
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Quote:
 Originally Posted by skipjack The points (0, 0), (4, -2), (6, 2), and (2, 4) are the vertices of a square whose diagonals have length 2√10. Hence the desired vector is (1/2)<6, 2> or (1/2)<2, -6>, i.e. <3, 1>, or <1, -3>.
original post said $|v| = 10$, not $\sqrt{10}$ ... October 13th, 2018, 08:54 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,927 Thanks: 2205 Thanks. The coordinates I gave should therefore be multiplied by √10. Tags find, 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 blacklisted Calculus 1 October 22nd, 2014 03:34 PM OriaG Calculus 1 May 22nd, 2013 09:14 AM miran97 Algebra 4 March 11th, 2013 12:14 PM rnck Advanced Statistics 1 August 21st, 2011 08:12 PM al1850 Calculus 4 May 3rd, 2008 04:04 PM

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