In △ X Y Z , X Y → = x and Y Z → = y and W Z = 1 4 X Z . Find in terms of x and y X Z → .

Given, Here, X Y = x and Y Z = y 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 △ X Y Z , X Z → = X Y → + Y Z → ∴ X Z → = x + y Hence, the answer is x + y

In △ X Y Z , X Y → = x and Y Z → = y and W Z = 1 4 X Z . Find in terms of x and y X W → .

Given, Here, X Y = x and Y Z = y . Also, W Z = 1 4 X Z 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 △ X Y Z , X Z → = X Y → + Y Z → ∴ X Z → = x + y Now, X W → = X Z → - W Z → ⇒ X W → = x + y - 1 4 x + y ⇒ X W → = x + y - 1 4 x - 1 4 y ⇒ X W → = 4 x - x 4 + 4 y - y 4 ⇒ X W → = 3 x 4 + 3 y 4 ⇒ X W → = 3 4 x + y Hence, the answer is 3 4 x + y

In △ X Y Z , X Y → = x and Y Z → = y and W Z = 1 4 X Z . Find in terms of x and y Y W → .

Given, Here, X Y = x and Y Z = y . Also, W Z = 1 4 X Z 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 △ X Y Z , X Z → = X Y → + Y Z → ∴ X Z → = x + y Now, X W → = X Z → - W Z → ⇒ X W → = x + y - 1 4 x + y ⇒ X W → = x + y - 1 4 x - 1 4 y ⇒ X W → = 4 x - x 4 + 4 y - y 4 ⇒ X W → = 3 x 4 + 3 y 4 ⇒ X W → = 3 4 x + y Now, consider △ X Y Z , apply the triangle law of vector addition, we get Y W → = X W → - X Y → ⇒ Y W → = 3 4 x + 3 4 y - x ⇒ Y W → = 3 x 4 - 4 x 4 + 3 4 y ⇒ Y W → = - x 4 + 3 4 y Hence, the answer is - x 4 + 3 4 y

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 A B → .

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 △ O B A , A B → = O B → - O A → ∴ A B → = 2 q - 2 p Hence, the answer is 2 q - 2 p

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

Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7

Author:Karen Morrison & Nick Hamshaw

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7

Attempt the free practice questions from Exercise 7: Exercise 23.7 with hints and solutions to strengthen your understanding. Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition solutions are prepared by Experienced Embibe Experts.

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7 with Hints & Solutions

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 4

In the diagram, $B C E$ and $A C D$ are straight lines. $\vec{A B} = 2 a$ and $\vec{B C} = 3 b$ . The point $C$ divides $A D$ in the ratio $2 : 1$ and divides $B E$ in the ratio $3 : 1$ . Express in terms of $a$ and $b$ , the vector $\vec{C E}$ .

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MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 4

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EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 5

In $△ X Y Z, \vec{X Y} = x$ and $\vec{Y Z} = y$ and $W Z = \frac{1}{4} (X Z)$ . Find in terms of $x$ and $y$ $\vec{X Z}$ .

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MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 5

In $△ X Y Z, \vec{X Y} = x$ and $\vec{Y Z} = y$ and $W Z = \frac{1}{4} (X Z)$ . Find in terms of $x$ and $y$ $\vec{X W}$ .

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MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 23 - Vectors and Transformations>Exercise 23.7>Q 5

In $△ X Y Z, \vec{X Y} = x$ and $\vec{Y Z} = y$ and $W Z = \frac{1}{4} (X Z)$ . Find in terms of $x$ and $y$ $\vec{Y W}$ .

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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 $q$ $\vec{A B}$ .

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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 $q$ $\vec{O N}$ .

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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 $q$ $\vec{M N}$ .

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Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 7: Exercise 23.7 with Hints & Solutions

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