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- Question 1, Exercise 3.2
- Question 2, Exercise 3.2
- Question 3 & 4, Exercise 3.2
- Question 5 & 6, Exercise 3.2
- Question 7, Exercise 3.2
- Question 7, Exercise 3.2
- Question 9 & 10, Exercise 3.2
- Question 11, Exercise 3.2
- Question 12, 13 & 14, Exercise 3.2
- Question 1, Exercise 3.3
- Question 2 and 3 Exercise 3.3
- Question 4 and 5 Exercise 3.3
- Question 6 Exercise 3.3
- Question 7 & 8 Exercise 3.3
- Question 9 & 10, Exercise 3.3
- Question 11, Exercise 3.3
- Question 12 & 13, Exercise 3.3
- Question 1 Exercise 3.4
- Question 2 Exercise 3.4
- Question 3 Exercise 3.4
- Question 4 Exercise 3.4
- Question 5 Exercise 3.4
- Question 6 Exercise 3.4
- Question 7 & 8 Exercise 3.4
- Question 9 Exercise 3.4
- Question 1 & 2 Exercise 3.5
- Question 3 & 4 Exercise 3.5
- Question 5(i) & 5(ii) Exercise 3.5
- Question 5(iii) & 5(iv) Exercise 3.5
- Question 6 Exercise 3.5
- Question 7 Exercise 3.5
- Question 8 Exercise 3.5
- Question 9 Exercise 3.5
- Question 1 Review Exercise 3
- Question 2 & 3 Review Exercise 3
- Question 4 & 5 Review Exercise 3
- Question 6 & 7 Review Exercise 3
- Question 8 & 9 Review Exercise 3
- Question 10 Review Exercise 3
Fulltext results:
- Question 1, Exercise 3.2
- ====== Question 1, Exercise 3.2 ====== Solutions of Question 1 of Exercise 3.2 of Unit 03: Matrices an... i}+3\hat{j}$, then find $\vec{a}+2\vec{b}$. ====Solution==== \begin{align}\vec{a}+2\vec{b}&=3\hat{i}-... }+3\hat{j}$, then find $3\vec{a}-2\vec{b}$. ====Solution==== \begin{align}3\vec{a}-2\vec{b}&=3(3\hat{... +3\hat{j}$, then find $2(\vec{a}-\vec{b})$. ====Solution==== First we have, \begin{align}\vec{a}-\vec
- Question 2, Exercise 3.2
- ====== Question 2, Exercise 3.2 ====== Solutions of Question 2 of Exercise 3.2 of Unit 03: Vectors. Th... the same direction as the vector $3\hat{i}.$ ====Solution==== Let $$\overset{\scriptscriptstyle\right... direction as the vector $3\hat{i}-4\hat{j}.$ ====Solution==== Let $$\overset{\scriptscriptstyle\right... ion as the vector $\hat{i}+\hat{j}-2\hat{k}.$ ====Solution==== Let $$\overset{\scriptscriptstyle\right
- Question 7, Exercise 3.2
- ====== Question 7, Exercise 3.2 ====== Solutions of Question 7 of Exercise 3.2 of Unit 03: Vectors. Thi... rrightarrow{PQ}$, if $P(-1,2)$, $Q(2,-1)$. ====Solution==== As we have \begin{align}\overrightarrow... \overrightarrow{PQ}.$ If $P(-2,1),Q(2,3).$ ====Solution==== Do yourself. =====Question 7(iii)===== ... htarrow{PQ}$. if $P(-1,1,2)$, $Q(2,-1,3)$. ====Solution==== As we have \begin{align}\overrightarrow{
- Question 7, Exercise 3.2
- ====== Question 7, Exercise 3.2 ====== Solutions of Question 7 of Exercise 3.2 of Unit 03: Vectors. Thi... rrightarrow{PQ}$, if $P(-1,2)$, $Q(2,-1)$. ====Solution==== As we have \begin{align}\overrightarrow... \overrightarrow{PQ}.$ If $P(-2,1),Q(2,3).$ ====Solution==== Do yourself. =====Question 7(iii)===== ... htarrow{PQ}$. if $P(-1,1,2)$, $Q(2,-1,3)$. ====Solution==== As we have \begin{align}\overrightarrow{
- Question 2 and 3 Exercise 3.3
- ====== Question 2 and 3 Exercise 3.3 ====== Solutions of Question 2 and 3 of Exercise 3.3 of Unit 03: ... \quad \vec{b}=2 \hat{i}+\hat{j}-7 \hat{k}$$. ====Solution==== We first find the sum \begin{align}\vec{... {j}+\hat{k}, \quad-\hat{i}+\hat{j}+2 \hat{k}$ ====Solution==== Let $\vec{a}=\hat{i}-\hat{j}+\hat{k}$ an... \hat{i}+4 \hat{j}, \quad 2 \hat{j}-5 \hat{k}$ ====Solution==== Let $\vec{a}=3 \hat{i}+4 \hat{j}$ and $\
- Question 12, 13 & 14, Exercise 3.2
- ====== Question 12, 13 & 14, Exercise 3.2 ====== Solutions of Question 12, 13 & 14 of Exercise 3.2 of U... pha \hat{i}+(\alpha +1)\hat{j}+2\hat{k}|=3$. ====Solution==== We are given \begin{align}|\alpha \hat{i... e sides of a triangle. Find the value of $z.$ ====Solution==== {{ :fsc-part1-kpk:sol:unit03:math-11-kpk-3-2-q13.svg?nolink |Question 13}} By head to tail ru
- Question 1, Exercise 3.3
- ====== Question 1, Exercise 3.3 ====== Solutions of Question 1 of Exercise 3.3 of Unit 03: Vectors. Th... }-5 \hat{k}$ then find $\vec{a}\cdot \vec{b}$ ====Solution==== \begin{align}\vec{a} \cdot \vec{b}&=(3 \... 5 \hat{k}$ then find $\vec{a} \cdot \vec{c}$. ====Solution==== \begin{align}\vec{a} \cdot \vec{c}&=(3 \... }$ then find $\vec{a} \cdot(\vec{b}+\vec{c})$ ====Solution==== \begin{align}\vec{b}+\vec{c}&=(\hat{i}-\
- Question 7 & 8 Exercise 3.3
- ====== Question 7 & 8 Exercise 3.3 ====== Solutions of Question 7 & 8 of Exercise 3.3 of Unit 03: Vect... {a}$ on $\vec{b}$ and $\vec{b}$ on $\vec{a}$. ====Solution==== $\vec{a}=-\dfrac{3}{2} \hat{j}+\dfrac{4}... {a}$ on $\vec{b}$ and $\vec{b}$ on $\vec{a}$. ====Solution==== We compute the dot product\\ \begin{alig... \hat{i}+\hat{j}+\hat{k}$ makes with $y$ axis. ====Solution==== Let $\vec{a}=\sqrt{2} \hat{i}+\hat{j}+\h
- Question 4 Exercise 3.4
- ====== Question 4 Exercise 3.4 ====== Solutions of Question 4 of Exercise 3.4 of Unit 03: Vectors. Thi... \hat{k},\quad$ find $\vec{a} \times \vec{b}$ ====Solution==== \begin{align}\vec{a} \times \vec{b}&=\le... \hat{k},\quad$ find $\vec{b} \times \vec{c}$ ====Solution==== \begin{align}\vec{b} \times \vec{c}&=\le... d $(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})$ ====Solution==== \begin{align}\vec{a}+\vec{b}&=(3 \vec{i}
- Question 7 & 8 Exercise 3.4
- ====== Question 7 & 8 Exercise 3.4 ====== Solutions of Question 7 & 8 of Exercise 3.4 of Unit 03: Vect... c{B} \times \vec{C}=\vec{C} \times \vec{A}.$$ ====Solution==== We are given\\ $$\vec{A}+\vec{B}+\vec{C}... and $\vec{b}=-2 \hat{i}+\hat{j}-3 \hat{k}$\\ ====Solution==== Let $\hat{n}$ be unit vector perpendicul... }=4 \hat{i}-2 \hat{j}-4 \hat{k} \text {. }$$ =====Solution===== Let $\hat{n}$ be unil vector perpendicu
- Question 7 Exercise 3.5
- ====== Question 7 Exercise 3.5 ====== Solutions of Question 7 of Exercise 3.5 of Unit 03: Vectors. Thi... k} \cdot \vec{w}=3 \hat{i}+\hat{j}+c \hat{k}$ ====Solution==== The given vectors are coplanar, therefor... hat{k}, \vec{w}=c \hat{i}+\hat{j}-c \hat{k}$. ====Solution==== The given vectors are coplanar, therefor... {k}$. $\vec{n}=c \hat{i}+2 \hat{j}+6 \hat{k}$ ====Solution==== Since the given vectors are coplanar, th
- Question 3 & 4, Exercise 3.2
- ====== Question 3 & 4, Exercise 3.2 ====== Solutions of Question 3 & 4 of Exercise 3.2 of Unit 03: Vect... d $q$ such that $\vec{r}=p\vec{a}+q\vec{b}$. ====Solution==== Given $$\vec{r}=p\vec{a}+q\vec{b}.$$ We ... value of $x$ such that $|\vec{p}+\vec{q}|=5.$ ====Solution==== We calculate \begin{align}\vec{p}+\vec{... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit03:ex3-2-p2 |< Question 2 ]]</btn></text> <te
- Question 5 & 6, Exercise 3.2
- ====== Question 5 & 6, Exercise 3.2 ====== Solutions of Question 5 & 6 of Exercise 3.2 of Unit 03: Vect... r in the direction of $\overrightarrow{AB}$. ====Solution==== The position vector of $\vec{A}$ and $\v... $(0,5).$ find coordinates of the vertex $D.$ ====Solution==== Position vectors of given points are $$\... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit03:ex3-2-p3 |< Question 3 & 4 ]]</btn></text>
- Question 9 & 10, Exercise 3.2
- ====== Question 9 & 10, Exercise 3.2 ====== Solutions of Question 9 & 10 of Exercise 3.2 of Unit 03: Ve... }-\overrightarrow{b}+3\overrightarrow{c}.$ ====Solution==== We compute that\\ \begin{align}2\overrig... the ratio $2:1$ internally and externally. ====Solution==== We find the position vector of a point $... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit03:ex3-2-p6 |< Question 8 ]]</btn></text> <te
- Question 11, Exercise 3.2
- ====== Question 11, Exercise 3.2 ====== Solutions of Question 11 of Exercise 3.2 of Unit 03: Vectors. T... t{i}+\hat{j}$ in the ratio $2:5$ internally. ====Solution==== Position vector of $C$ is $\overrightarr... {i}+2\hat{j}$ in the ratio $4:3$ externally. ====Solution==== Position vector of $E$ is $\overrightarr... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit03:ex3-2-p7 |< Question 9 & 10 ]]</btn></text