O A C B is a parallelogram in which O A → = 2 p and O B → = 2 q . M is the midpoint of B C and N is the midpoint of A C . Find in terms of p and q O N → .

Here, we have Here, O B → = 2 q and O A → = 2 p . 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 Consider △ A O N , Since N is the mid point of A C , A N = 1 2 A C . Also, O B = A C . So, A N = q O N → = A O → + A N → ∴ O N → = 2 p + q Hence, the answer is 2 p + q

O A C B is a parallelogram in which O A → = 2 p and O B → = 2 q . M is the midpoint of B C and N is the midpoint of A C . Find in terms of p and q O N → .

Here, we have Here, O B → = 2 q and O A → = 2 p . 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 Consider △ A O N , Since N is the mid point of A C , A N = 1 2 A C . Also, O B = A C . So, A N = q O N → = A O → + A N → ∴ O N → = 2 p + q Hence, the answer is 2 p + q

O A C B is a parallelogram in which O A → = 2 p and O B → = 2 q . M is the midpoint of B C and N is the midpoint of A C . Find in terms of p and q M N → .

Here, we have Here, O B → = 2 q and O A → = 2 p . Consider △ M N C , Since N is the mid point of A C , N C = 1 2 A C . Also, O B = A C . So, N C = q Also, M is the mid point of B C , M C = 1 2 B C . Also, B C = O A So, M C = p 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 M N → = M C → - N C → ∴ M N → = p - q Hence, the answer is p - q

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 6

EASY

Upper Secondary: IGCSE

IMPORTANT

Earn 100

$O A C B$ is a parallelogram in which $\vec{O A} = 2 p$ and $\vec{O B} = 2 q$ . $M$ is the midpoint of $B C$ and $N$ is the midpoint of $A C$ . Find in terms of $p$ and $q$ $\vec{O N}$ .

Important Questions on Vectors and Transformations

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 6

$O A C B$ is a parallelogram in which $\vec{O A} = 2 p$ and $\vec{O B} = 2 q$ . $M$ is the midpoint of $B C$ and $N$ is the midpoint of $A C$ . Find in terms of $p$ and $q$ $\vec{M N}$ .