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- Question 1, Exercise 3.2
- -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $\vec{a}+2\vec{b}$. ====Solution==== \begin{ali... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $3\vec{a}-2\vec{b}$. ====Solution==== \begin{al... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $2(\vec{a}-\vec{b})$. ====Solution==== First we... -5\hat{j}$ and $\vec{b}=-2\hat{i}+3\hat{j}$, then find $|\vec{a}+\vec{b}|$. ====Solution==== We have,
- Question 2, Exercise 3.2
- TBB) Peshawar, Pakistan. =====Question 2(i)===== Find unit vector having the same direction as the vect... required unit vector. =====Question 2(ii)===== Find unit vector having the same direction as the vect... required unit vector. =====Question 2(iii)===== Find unit vector having the same direction as the vect... ich is the unit vector. =====Question 2(iv)===== Find unit vector having the same direction as the vect
- Question 7, Exercise 3.2
- TBB) Peshawar, Pakistan. =====Question 7(i)===== Find the components and the magnitude of $\overrightar... gnitude is $3\sqrt{2}$. =====Question 7(ii)===== Find the components and the magnitude of $\overrightar... ution==== Do yourself. =====Question 7(iii)===== Find the components and the magnitude of $\overrightar... nitude is $\sqrt{14}$. =====Question 7(iv)===== Find the components and the magnitude of $\overrightar
- Question 7, Exercise 3.2
- TBB) Peshawar, Pakistan. =====Question 7(i)===== Find the components and the magnitude of $\overrightar... gnitude is $3\sqrt{2}$. =====Question 7(ii)===== Find the components and the magnitude of $\overrightar... ution==== Do yourself. =====Question 7(iii)===== Find the components and the magnitude of $\overrightar... nitude is $\sqrt{14}$. =====Question 7(iv)===== Find the components and the magnitude of $\overrightar
- Question 9 & 10, Exercise 3.2
- nd $\overrightarrow{c}=\hat{i}-2\hat{j}+\hat{k}$, find a vector of magnitude of $6$ unit which is parall... tor with given conditions. =====Question 10===== Find the position vector of a point $R$ which divides ... internally and externally. ====Solution==== We find the position vector of a point $R$ which divides ... }{3}\hat{j}+\dfrac{1}{3}\hat{k}\end{align} Now we find the position vector of a point $\vec{R}$, which d
- Question 1, Exercise 3.3
- k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a}\cdot \vec{b}$ ====Solution==== \begin{al... k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a} \cdot \vec{c}$. ====Solution==== \begin{... k}$ and $\vec{c}=2\hat{i}+\hat{j}-5 \hat{k}$ then find $\vec{a} \cdot(\vec{b}+\vec{c})$ ====Solution====... 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
- i}+\hat{j}-7 \hat{k}$$. ====Solution==== We first find the sum \begin{align}\vec{a}+\vec{b}&=(2 \hat{i}+... j}-12\hat{k})\end{align} =====Question 3(i)===== Find the angles between the pairs of vectors: $\hat{i}... a=90^{\prime \prime}$$. =====Question 3(ii)===== Find the angles between the pairs of vectors: $3 \hat{... oximately)}\end{align} =====Question 3(iii)===== Find the angles between the pairs of vectors: $2 \hat{
- Question 9 Exercise 3.4
- BB) Peshawar, Pakistan. =====Question 9(i)===== Find the area of parallelogram whose diagonals are $\v... t sides $\vec{c}$ and $\vec{d}$ which are used to find the area of parallelogram.\\ $E$ is the intersect... 110} \text { units. }$$ =====Question 9(ii)===== Find the area of parallelogram whose diagonals are $\v... t sides $\vec{c}$ and $\vec{d}$ which are used to find the area of parallelogram.\\ $E$ is the intersect
- Question 5 & 6, Exercise 3.2
- KPTBB) Peshawar, Pakistan. =====Question 5===== Find the length of the vector $\overrightarrow{AB}$ fr... the point $\vec{A}(-3,5)$ to $\vec{B}(7,9)$. Also find the unit vector in the direction of $\overrightar... espectively given by $(-2,-3),(1,4)$ and $(0,5).$ find coordinates of the vertex $D.$ ====Solution==== P
- Question 1 Exercise 3.4
- TBB) Peshawar, Pakistan. =====Question 1(i)===== Find the cross product $\hat{j} \times(2 \hat{j}+3 \ha... }=3 \hat{i}.\end{align} =====Question 1(ii)===== Find the cross product $(2 \hat{i}-3 \hat{j}) \times \... 2 \hat{j} .\end{align} =====Question 1(iii)===== Find the cross product $(2 \hat{i}-3 \hat{j}+5 \hat{k}
- Question 4 Exercise 3.4
- quad \vec{c}=\hat{i}+\hat{j} \quad \hat{k},\quad$ find $\vec{a} \times \vec{b}$ ====Solution==== \begin{... \quad\vec{c}=\hat{i}+\hat{j} \quad \hat{k},\quad$ find $\vec{b} \times \vec{c}$ ====Solution==== \begin{... \quad\vec{c}=\hat{i}+\hat{j} \quad \hat{k},\quad$ find $(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})$ ====S
- Question 7 & 8 Exercise 3.4
- \vec{A} \text {. }$$\\ =====Question 8 (i)===== Find a unit vector perpendicular to both $\vec{a}=\hat... vec{a}$ and $\vec{b}$. =====Question 8 (ii)===== Find a unit vector perpendicular to both Find a vector of magnitude 10 and perpendicular to both $$\vec{a}=2
- Question 8 Exercise 3.5
- TBB) Peshawar, Pakistan. =====Question 8(i)===== Find the volume of tetrahedron with the Vectors as cot... t { units. }\end{align} =====Question 8(ii)===== Find the volume of tetrahedron with $A(2,3,1), B(-1,-2... f $D, \overrightarrow{O D}=\hat{j}-2 \hat{k}$ We find the edges vectors \begin{align}\vec{a}&=\overrigh
- Question 4 & 5 Review Exercise 3
- If $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$, then find $(\vec{r} \times \hat{i}) \cdot(\bar{r} \times \hat{j})+x y$ ====Solution==== We have to find\\ $$(\vec{r} \times \hat{i}) \cdot(\vec{r} \times... and $\vec{b}=2 \hat{i}+6 \hat{j}+3 \hat{k}$, then find the projection of $\vec{a}$ on $\vec{b}$. ====Sol
- Question 11, Exercise 3.2
- BB) Peshawar, Pakistan. =====Question 11(i)===== Find the position vectors of the point of division of ... }{7}\hat{j}\end{align} =====Question 11(ii)===== Find the position vectors of the point of division of