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- Question 10 Review Exercise 3
- ^2+|\vec{c}|^2 -2|\vec{b}|| \vec{c}| \cos A$. ====Solution==== Let considering a triangle $A B C$ as shown i... \vec{a}|= |\vec{b}| \cos C+| \vec{c}| \cos B$ ====Solution==== Let consider three vectors $\vec{a}, \vec{b}$
- Question 8 & 9 Review Exercise 3
- hose vertices are $(0,0,2),(-1,3,2),(1,0,4)$. ====Solution==== Lel $A(0,0,2)$, $B(-1,3,2)$ and $C(1,0,4)$. ... d$ $C(4,-2,2)\quad$ and $\quad D(0,-8,-2)$.\\ ====Solution==== \begin{align}\text { Let } \vec{a} &=\overrig
- Question 6 & 7 Review Exercise 3
- c{c}=\lambda \hat{j}+3 \hat{k}$ are coplanar. ====Solution==== Since the given vectors are coplanar, therefo... te the angle between $\vec{a}$ and $\vec{b}$. ====Solution==== Let $\theta$ be the angle between two vectors
- Question 2 & 3 Review Exercise 3
- mu \hat{k})=\overrightarrow{0} \text {. }$$\\ ====Solution==== We are given\\ \begin{align}(\hat{i}+3 \hat{j... unit vector parallel to $\vec{a}+\vec{b}$.\\ ====Solution==== Let $\hat{n}$ be unit normal in direction of
- Question 4 & 5 Review Exercise 3
- s \hat{i}) \cdot(\bar{r} \times \hat{j})+x y$ ====Solution==== We have to find\\ $$(\vec{r} \times \hat{i}) ... ind the projection of $\vec{a}$ on $\vec{b}$. ====Solution==== We have to compute Projection of $\vec{a}$ o
- Question 9 Exercise 3.5
- i} \times \hat{j}). \hat{k}+\hat{i}. \hat{j}$ ====Solution==== \begin{align} (\hat{i} \times \hat{j}) \cdot ... \hat{j}) \cdot \hat{i}+\hat{j} \cdot \hat{k}$ ====Solution==== \begin{align} (\hat{k} \times \hat{j}) \cdot
- Question 7 Exercise 3.5
- k} \cdot \vec{w}=3 \hat{i}+\hat{j}+c \hat{k}$ ====Solution==== The given vectors are coplanar, therefore \be... hat{k}, \vec{w}=c \hat{i}+\hat{j}-c \hat{k}$. ====Solution==== The given vectors are coplanar, therefore \be... {k}$. $\vec{n}=c \hat{i}+2 \hat{j}+6 \hat{k}$ ====Solution==== Since the given vectors are coplanar, therefo
- Question 8 Exercise 3.5
- }, \\ \vec{c}&=7 \hat{j}+8 \hat{k}\end{align} ====Solution==== The volume of tetrahedron is \begin{align}V&=... ,-2,0)$, $C(0.2,-5) . D(0.1,-2)$ as vertices. ====Solution==== Position vector of $A,\overrightarrow{O A}=2
- Question 6 Exercise 3.5
- )$, $(2.2,-5)$ and $(3.5 .0)$ lie in a plane? ====Solution==== Let we denote the given points with $A(4,-2,1
- Question 5(iii) & 5(iv) Exercise 3.5
- $(\vec{a}. \vec{b})^2,\quad|a|^2,\quad|b|^2$ ====Solution==== \begin{align}\vec{a} \cdot \vec{b}&=(a_1 \hat... b} \cdot \vec{b})-(\vec{a} \cdot \vec{b})^2$. ====Solution==== We have already calculated L.H.S in (ii) tha
- Question 5(i) & 5(ii) Exercise 3.5
- is orthogonal to both $\vec{a}$ and $\vec{b}$ ====Solution==== To show that $\vec{a} \times \vec{b}$ is orth... es \vec{b}$ and $|\vec{a} \times \vec{b}|^2$ ====Solution==== We know that \begin{align}\vec{a}\times \vec{
- Question 3 & 4 Exercise 3.5
- c{c}=-\vec{c} \times \vec{b} \cdot \vec{a}$\\ ====Solution==== \begin{align}\vec{a} \cdot \vec{b} \times \ve... {k}\quad$ and $\quad\hat{k}-\hat{i}$ is zero. ====Solution==== Let $$\vec{a}=\hat{i}-\hat{j}, \vec{b}=\hat{
- Question 9 Exercise 3.4
- \quad\vec{b}=-2 \hat{i}+3 \hat{j}+4 \hat{k}$. ====Solution==== We are give the diagonal as shown in figure, ... nd $\quad\vec{h}=\hat{i}-3 \hat{j}+4 \hat{k}$ ====Solution==== We are given the diagonals as shown in figure
- Question 1 & 2 Exercise 3.5
- ec{c}=3 \hat{i}+\hat{j}+2 \hat{k} \text {. }$ ====Solution==== We know that \begin{align}V&=\vec{a} \cdot \v... nd $\quad\vec{c}=\hat{i}-3 \hat{j}-4 \hat{k}$ ====Solution==== The volume of parallelopiped is: \begin{align
- Question 7 & 8 Exercise 3.4
- c{B} \times \vec{C}=\vec{C} \times \vec{A}.$$ ====Solution==== We are given\\ $$\vec{A}+\vec{B}+\vec{C}=\vec... and $\vec{b}=-2 \hat{i}+\hat{j}-3 \hat{k}$\\ ====Solution==== Let $\hat{n}$ be unit vector perpendicular to... }=4 \hat{i}-2 \hat{j}-4 \hat{k} \text {. }$$ =====Solution===== Let $\hat{n}$ be unil vector perpendicular t