December 29th, 2018, 02:16 PM  #1 
Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2  Application of vectorial knowledge
I was ask to prove some theorems using my knowledge on vector; please can anyone help me on how to go about this 1. Prove that the diagonals of a rhombus meet at a right angle 2. Prove that the diagonal of a square makes an angle of 45 degrees with all sides 3. Prove the diagonals of a rectangle are equal 4. Prove that the adjacent side of a kite are equal How am I supposed to prove all this using vectors, please can anyone help me, am seriously in need of how to do it...? Last edited by skipjack; December 31st, 2018 at 12:13 AM. 
December 29th, 2018, 02:25 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659 
I don't know what the requirement (knowledge on vector) means. However: 1) Symmetry 2) diagonals are angle bisectors 3) symmetry or Pythagorean theorem twice 4) definition of kite? 
December 29th, 2018, 02:59 PM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,314 Thanks: 1230  
December 29th, 2018, 08:50 PM  #4 
Member Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 
Please show me a sample with the previous ones...

December 30th, 2018, 03:18 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659  
December 30th, 2018, 04:18 PM  #6 
Newbie Joined: Dec 2018 From: Euclidean Plane Posts: 7 Thanks: 3 
Here's how you might get started for problem 1: A rhombus is a parallelogram, all of whose sides are equal in length. If we want to think of this in terms of vectors, consider two vectors $\vec{v_1}$ and $\vec{v_2}$. If you draw a picture of this, you will see that $\vec{v_1} + \vec{v_2}$ will be the diagonal of a parallelogram formed by these two vectors. The other diagonal will be $\vec{v_1}  \vec{v_2}$ (or equivalently, $\vec{v_2}  \vec{v_1}$). This is a rhombus if $ \vec{v_1} =  \vec{v_2}$. So how can you tell if the two diagonals ($\vec{v_1} + \vec{v_2}$) and ($\vec{v_1}  \vec{v_2}$) are perpendicular to each other? (Hint: think dot product.) 
December 30th, 2018, 04:18 PM  #7 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,042 Thanks: 815 Math Focus: Wibbly wobbly timeywimey stuff.  

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