Question

На стороне ВС ромба АВСD лежит точка К так, что ВК равно КС, о - точка пересечения диагоналей.выразите векторы АО, АК, КD через векторы аравно АВ, б равно АD пожалуйста, помогите

Answer 1

AO=1/2*AC=1/2*(AB+BC)=1/2*(a+b)=(a+b)/2
AK=AB+BK=a+b/2
KD=KA+AD=-AK+AD=-(a+b/2)+b=-a-b/2+b=-a+b/2

Answer 2

Given Information

We are given that point K lies on the side AB of rhombus ABCD such that VK is equal to KS. We are asked to express vectors AO, AK, and KD in terms of vectors AB and AD.

Solution

To express vectors AO, AK, and KD in terms of vectors AB and AD, we can use the properties of a rhombus.

1. Vector AO: - Since a rhombus has opposite sides that are parallel and equal in length, we can say that vector AO is equal to vector OB. - Therefore, AO = OB.

2. Vector AK: - Since VK is equal to KS, we can say that vector AK is equal to vector AB minus vector BK. - Since BK is equal to vector KD, we can say that vector AK is equal to vector AB minus vector KD. - Therefore, AK = AB - KD.

3. Vector KD: - Since a rhombus has opposite sides that are parallel and equal in length, we can say that vector KD is equal to vector AD. - Therefore, KD = AD.

To summarize: - AO = OB - AK = AB - KD - KD = AD

Please let me know if you need any further clarification.