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- Question 12, 13 & 14, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... t03:math-11-kpk-3-2-q13.svg?nolink |Question 13}} By head to tail rule of vectors addition, we have\\ ... }+3\hat{k}&=\hat{i}+6\hat{j}-z\hat{k}\end{align} By comparison $\hat{i},\hat{j}$ and $\hat{k}.$ we ha... \overrightarrow{CD}&=-3\overrightarrow{AB} \text{ by using (i)}\end{align} This gives $$\overrightarro
- Question 10 Review Exercise 3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... as shown in figure, whose sides are represented by $\vec{a}, \vec{b}$ and $\vec{c}$. By head to tail rule. we get \begin{align} \vec{b}&=\vec{a}+\vec{... d $\vec{c}$ are represented respectively in order by sides $B C, C A$ and $AB$ of $\triangle A B C$.\\
- Question 3 & 4, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... s \hat{i}-9\hat{j}=(p+5q)\hat{i}+(2p-q)\hat{j}.$$ By comparing the coeffients of $\hat{i}$ and $\hat{j... ve, $$p+5q=1…(i)$$ $$2p-q=-9 …(ii)$$ Multiply $2$ by (i) and subtract (ii) from (i). We have \[\begin{
- Question 5 & 6, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... of the vertices $A, B$ and $C$ respectively given by $(-2,-3),(1,4)$ and $(0,5).$ find coordinates of ... hat{i}+7\hat{j}=-x\hat{i}+(5-y)\hat{j}\end{align} By comparison, we have $$3=-x \text{ and } 7=5-y$$ T
- Question 9 & 10, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... h divides the line joining the points internally. By using ratio theorem, we have \begin{align}\overri... h divides the line joining the points externally. By using ratio theorem, we have \begin{align}\overri
- Question 11, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... overline{CD}$ in the ratio $2:5$internally, then by ratio theorem, we have position vector $H$ is: \b... overline{EF}$ externally in the ratio $4:3$, then by ratio theorem, \begin{align}\overrightarrow{OK}&=
- Question 11, Exercise 3.3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... =|\vec{b}|^2\\ 14+21&=35\\ 35&=35\end{align} Thus by Pytagorous theorem, the vectors $\vec{a}, \vec{b}... quad \vec{a} \cdot \vec{c}$. or sides represented by $\vec{a}$ and $\vec{c}$ form right angle with eac
- Question 3 Exercise 3.4
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... orthogonal to both $\vec{a}$ and $\vec{b}$. then by cross product\\ \begin{align}\hat{n}&=\dfrac{\vec... orthogonal to buth $\vec{a}$ and $\vec{b}$. then by cross product we have\\ \begin{align}\hat{n}&=\df
- Question 9 Exercise 3.4
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... +2 \hat{j}+ \hat{k} \text {. }....(2) \end{align} By using (1) and (2), we have,\\ \begin{align}\vec{c... i}-\dfrac{1}{2} \hat{j}+\hat{k}....(2)\end{align} By using (1) and (2), we have,\\ \begin{align}\vec{c
- Question 1, Exercise 3.2
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... =5\hat{i}-8\hat{j}\end{align} Multiply both sides by $2$. We have, $$2(\vec{a}-\vec{b})=10\hat{i}-16\
- Question 4 and 5 Exercise 3.3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... & 1 & -1 \end{array}\right| \end{align} expanding by $R_1$ we have \begin{align} & \vec{c}=(-2-1) \hat
- Question 9 & 10, Exercise 3.3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... align} =====Question 10===== Find the work done by the force $\vec{F}=2 \hat{i}+3 \hat{j}+\hat{k}$ i
- Question 12 & 13, Exercise 3.3
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... \vec{a}|^2+|\vec{c}|^2+\vec{b} \cdot \vec{a}\quad by \quad \vec{a} \cdot \vec{a}=|\vec{a}|^2 and\quad
- Question 1 & 2 Exercise 3.5
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... of the parallelopiped whose edges are represented by $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}, \vec{b}=2 \h
- Question 3 & 4 Exercise 3.5
- Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB)... \cdot 0+1.2=-25\end{align} Multiplying both sides by -1\\ $$-\vec{c} \times \vec{b} \cdot \vec{a}=25..