Question

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

Answer 1

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.

Answer 2

Answer:

Above is ur Answer

Step-by-step explanation:

Hope it helps u