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- Question 1, Exercise 3.2
- at{i}-5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $\vec{a}+2\vec{b}$. ====Solution==== \begi... at{i}-5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $3\vec{a}-2\vec{b}$. ====Solution==== \beg... at{i}-5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $2(\vec{a}-\vec{b})$. ====Solution==== Fir... at{i}-5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $|\vec{a}+\vec{b}|$. ====Solution==== We h
- Question 2, Exercise 3.2
- {\scriptscriptstyle\rightharpoonup}{a}=3\hat{i}$$ Then $$|\overset{\scriptscriptstyle\rightharpoonup}{a}... criptstyle\rightharpoonup}{a}=3\hat{i}-4\hat{j}$$ Then $$|\overset{\scriptscriptstyle\rightharpoonup}{a}... \rightharpoonup}{a}=\hat{i}+\hat{j}-2\hat{k}$$ \\ Then \\ $$|\overset{\scriptscriptstyle\rightharpoonup}... frac{\sqrt{3}}{2}\hat{i}-\dfrac{1}{2}\hat{j}$$ \\ Then \\ $$|\overset{\scriptscriptstyle\rightharpoonup}
- Question 1, Exercise 3.3
- \hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a}\cdot \vec{b}$ ====Solution==== \beg... \hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a} \cdot \vec{c}$. ====Solution==== \b... \hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a} \cdot(\vec{b}+\vec{c})$ ====Solutio... \hat{k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $(\vec{a}-\vec{b})\cdot\vec{c}$ ====Solution
- Question 2 and 3 Exercise 3.3
- nit vector $x$ the sum of $\vec{a}$ and $\vec{b}$ then \begin{align}\hat{c}&=\dfrac{\vec{a}+\vec{b}}{|\v... ween $\vec{a}$ and $\vec{b}$ \begin{align}\text { then } \cos \theta&=\dfrac{\vec{a} \cdot \vec{b}}{|\ve... ween $\vec{a}$ and $\vec{b}$ \begin{align}\text { then } \quad \cos \theta &=\dfrac{\vec{a} \cdot \vec{b... eta$ be the angle between $\vec{a}$ and $\vec{b}$ then $$\cos \theta=\dfrac{\vec{a} \cdot \vec{b}}{|\vec
- Question 7 & 8 Exercise 3.4
- tor perpendicular to both $\vec{a}$ and $\vec{b}$ then\\ \begin{align}\hat{n}&=\dfrac{\vec{a} \times \ve... tor perpendicular to both $\vec{a}$ and $\vec{b}$ then\\ \begin{align} \hat{n}=\dfrac{\vec{a} \times \ve... lar to both and having magnitude \\ $\vec{c} =10$ then\\ $\vec{c}= \vec{c} \cdot \hat{n}=10\left(\dfrac{
- Question 1 Review Exercise 3
- > iv. If $\mid \vec{a}+\vec{b}=\vec{a}-\vec{b}$. then * (a) $\vec{a} \| \vec{b}$ * %%(b)%% $\... on vectors of the vertices of a $\angle A A B C$. then $\vec{B} \cdot B^2 \cdot(\vec{i}$ * %%(a)%% ... between any two vectors $\vec{a}$ and $\vec{b}$. then $\vec{a} \cdot \vec{b} \mid=$ $\vec{a} \times \ve
- Question 11, Exercise 3.2
- nt $\overline{CD}$ in the ratio $2:5$internally, then by ratio theorem, we have position vector $H$ is:... nt $\overline{EF}$ externally in the ratio $4:3$, then by ratio theorem, \begin{align}\overrightarrow{OK
- Question 6 Exercise 3.3
- f $\vec{a}+m \vec{b}$ is orthogonal to $\vec{a}$, then \begin{align}(\vec{a}+m \vec{b}) \cdot \vec{a}&=0... f $\vec{a}+n \vec{b}$ is orthogonal to $\vec{b}$, then \begin{align}(\vec{a}+m \vec{b}) \cdot \vec{b}&=0
- Question 3 Exercise 3.4
- ector orthogonal to both $\vec{a}$ and $\vec{b}$. then by cross product\\ \begin{align}\hat{n}&=\dfrac{\... ector orthogonal to buth $\vec{a}$ and $\vec{b}$. then by cross product we have\\ \begin{align}\hat{n}&=
- Question 6 Exercise 3.4
- -2.2)$ relative to the origin that is $O(0,0,0)$, then\\ \begin{align}\vec{r}&=\overrightarrow{O P}\\ &=... ector of point $P(1,-2,2)$ relative to $A(1,2,1)$ then\\ \begin{align}\vec{r}&=\overrightarrow{A P}\\ &=
- Question 6 Exercise 3.5
- A(4,-2,1), B(5,1,6)$. $C(2,2,-5)$ and $D(3,5.0)$ then Position vector of $A, \overrightarrow{O A}=4 \ha... f $D, \overrightarrow{O D}=3 \hat{i}+5 \hat{j}$. Then \begin{align}\vec{a}&=\overrightarrow{A B}=\overr
- Question 2 & 3 Review Exercise 3
- at{k}$ and $\vec{b}=2 \hat{i}-2 \hat{j}-\hat{k}$, then find a unit vector parallel to $\vec{a}+\vec{b}$.... be unit normal in direction of $\vec{a}+\vec{b}$, then\\ \begin{align} \hat{n}&=\dfrac{\vec{a}+\vec{b}}{
- Question 4 & 5 Review Exercise 3
- ===== If $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$, then find $(\vec{r} \times \hat{i}) \cdot(\bar{r} \tim... {k}$ and $\vec{b}=2 \hat{i}+6 \hat{j}+3 \hat{k}$, then find the projection of $\vec{a}$ on $\vec{b}$. ==
- Question 3 & 4, Exercise 3.2
- \hat{i}-\hat{j}$ and $\vec{q}=x\hat{i}+3\hat{j},$ then find the value of $x$ such that $|\vec{p}+\vec{q}
- Question 5 & 6, Exercise 3.2
- vector in the direction of $\overrightarrow{AB}$. Then \begin{align}\hat{r}&=\dfrac{\overrightarrow{AB}}