a) The vector is represented by .
b) The vector is represented by .
c) The vector is represented by .
<h3 /><h3>Procedure - Vectors in a parallelogram </h3><h3>a) Vector
in terms of
</h3>
By geometry we know that diagonals in a parallelogram fulfill the following properties:
-
-
Hence, we have the following vectorial expressions:
- (1)
- (2)
- (3)
- (4)
Hence, we have the following vectorial expression for CA:
(5)
The vector is represented by .
<h3>b) Vector
in terms of
and
</h3>
The vector is defined by the following expression:
(6)
By (1) and (2):
(7)
The vector is represented by .
<h3>c) Vector
in terms of
and
</h3>
The vector is defined by the following expression:
(8)
By (5) and (7):
(9)
The vector is represented by .
<h3>Remark</h3>
The statement presents mistakes. Correct form is presented below:
<em>ABCD is a parallelogram. The diagonals of ABCD intersect at O. </em><em> and </em><em>.</em>
<em />
<em>a) </em><em>Express the vector </em><em> in terms of </em><em>.</em>
<em>b) </em><em>Express the vector </em><em> in terms of </em><em> and </em><em>.</em>
<em>c) </em><em>Express the vector </em><em> in terms of </em><em> and </em><em>.</em>
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