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 December 29th, 2018, 01:16 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 30th, 2018 at 11:13 PM.
 December 29th, 2018, 01:25 PM #2 Global Moderator   Joined: May 2007 Posts: 6,763 Thanks: 697 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? Thanks from topsquark
December 29th, 2018, 01:59 PM   #3
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Quote:
 Originally Posted by mathman I don't know what the requirement (knowledge on vector) means. However: 4) definition of kite?
a kite is a quadrilateral with pairs of adjacent sides equal in length.

think of a typical kite.

 December 29th, 2018, 07:50 PM #4 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 Please show me a sample with the previous ones...
December 30th, 2018, 02:18 PM   #5
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 Originally Posted by romsek a kite is a quadrilateral with pairs of adjacent sides equal in length. think of a typical kite.
That's what I thought. So 4) is true by definition.

 December 30th, 2018, 03:18 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, 03:18 PM   #7
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 Originally Posted by Harmeed Please show me a sample with the previous ones...
Tell you what.

You have been given much information about 4). Can you set up a proof for this one?

-Dan

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