Math, asked by Chahalsaab5356, 1 year ago

OABC is a parallelogram. If OA = a and OC = c, find the vector equation of the side BC.


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Answers

Answered by HappiestWriter012
41

Given,

OABC is a parallelogram.

OA = a

OC = c

By Parallelogram law of vectors which states, If two vectors are represented by the adjacent sides of a parallelogram both in magnitude and direction. Their resultant both in magnitude and direction is represented by their diagonal.

So,

 \overline{OA} +  \overline{OC} =  \overline{OB}

Therefore,

  \overline{OB} = a + c

Now,

From Triangle law, If two vectors form sides of a triangle taken in order , then their resultant is represented by the closing side taken in the reverse order.

By this,

 \overline{OB} +  \overline{BC}= \overline{ OC } \\ \\   \overline{BC}= \overline{ OC }  - \overline{OB}  \\  \\  \overline{BC}= \: c \:  - (a + c) \\  \\  \overline{BC}= - a

Therefore, BC is represented by - a

Vector equation of BC = - OA or, BC = OC - OB = OC - ( OA + OC ).

The same can be calculated by the fact that, Length of opposite sides in a parallelogram are same.

BC = AO

BC = - OA

BC = - a.

Answered by dupatisankar
3

Answer:

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