Mathematics for IGCSE & O level - Vectors (Section 1 - No. 5)
In a parallelogram OABC, \(\vec{OA} = \vec{a}\) and \(\vec{OC} = \vec{c}\). M is the midpoint of BC. Which of the following statements are true?
\(\vec{BC} = \vec{c}\)
\(\vec{OB} = \vec{a} + \vec{c}\)
\(\vec{AM} = \vec{c} - \frac{1}{2}\vec{a}\)
\(\vec{OM} = \frac{1}{2}\vec{a} + \vec{c}\)
Explanation
BC = OA = c and therefore, OB = OA + AB, also AB = OC = c, making OB = a+c, and OM = OB + BM = a+c + 1/2 OA= 1/2 a + c.
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