The diagram shows a quadrilateral O A B C . O A ⇀ = a , O C ⇀ = c and C B ⇀ = 2 a . X is a point on O B such that O X : X B = 1 : 2 . Find A C ⇀ and A X ⇀ in terms of a and c , in its simplest form

Given, Consider the △ C O A , O A → = a and O C → = c Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector. Thus, we get ⇒ A C → = - O A → + O C → ∴ A C → = - a + c Now, In △ O C B O B → = O C → + C B → O B → = c + 2 a Therefore, O X → = 1 3 O B → O X → = 1 3 ( c + 2 a ) Now, In △ O X A A X → = O X → - O A → A X → = 1 3 ( c + 2 a ) - a A X → = 1 3 c + 2 a 3 - a A X → = 1 3 c - 1 3 a A X → = 1 3 c - a A X → = 1 3 A C → Thus, A X → = 1 3 A C → and A C → = - a + c

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Examination practice>Q 2

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Earn 100

Draw the image of shape $A$ after a translation by vector $(\begin{matrix} 2 \\ - 3 \end{matrix})$

Important Questions on Vectors and Transformations

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Examination practice>Q 3

The diagram shows a quadrilateral $O A B C$ . $\overset{⇀}{O A} = a, \overset{⇀}{O C} = c$ and $\overset{⇀}{C B} = 2 a$ . $X$ is a point on $O B$ such that $O X : X B = 1 : 2$ . Find $\overset{⇀}{A C}$ and $\overset{⇀}{A X}$ in terms of $a$ and $c,$ in its simplest form

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EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Examination practice>Q 3

The diagram shows a quadrilateral $O A B C$ . $\overset{⇀}{O A} = a, \overset{⇀}{O C} = c$ and $\overset{⇀}{C B} = 2 a$ . $X$ is a point on $O B$ such that $O X : X B = 1 : 2$ . Explain why the vectors $\overset{⇀}{A C}$ and $\overset{⇀}{A X}$ show that $C, X$ and $A$ lie on a straight line.