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- Question 9 Exercise 3.4
- 9(i)===== Find the area of parallelogram whose diagonals are $\vec{a}=4 \hat{i}+\hat{j}-2 \hat{k}\quad... }+4 \hat{k}$. ====Solution==== We are give the diagonal as shown in figure, instead of two adjacent si... arallelogram.\\ $E$ is the intersection of two diagonals, so $E$ is the midpoint of both diagonals. Thus\\ \begin{align}\overrightarrow{A E}&=\overrightar
- Question 6 Exercise 3.3
- value of $m$ so that $\vec{a}+m \vec{b}$ is orthogonal to $\vec{a}$ ====Solution==== We know that \be... hat{k}\end{align}. If $\vec{a}+m \vec{b}$ is orthogonal to $\vec{a}$, then \begin{align}(\vec{a}+m \ve... value of $m$ so that $\vec{a}+m \vec{b}$ is orthogonal to $\vec{b}$. ====Solution==== If $\vec{a}+n \vec{b}$ is orthogonal to $\vec{b}$, then \begin{align}(\vec{a}+m \ve
- Question 3 Exercise 3.4
- uestion 3(i)===== Find a unit vector that is orthogonal to the given vector $\vec{a}=\hat{i}- 2 \hat{j... ===Solution==== Let $\hat{n}$ be unit vector orthogonal to both $\vec{a}$ and $\vec{b}$. then by cross... estion 3(ii)===== Find a unit vector that is orthogonal to the given vector $\vec{a}=3 \hat{i}-\hat{j}... ===Solution==== Let $\hat{n}$ be unit vector orthogonal to buth $\vec{a}$ and $\vec{b}$. then by cross
- Question 5(i) & 5(ii) Exercise 3.5
- $ and prove that $\vec{a} \times \vec{b}$ is orthogonal to both $\vec{a}$ and $\vec{b}$ ====Solution==== To show that $\vec{a} \times \vec{b}$ is orthogonal to both $\vec{a}$ and $\vec{b}$. We check the... and $\vec{b}$. For $\vec{a} \times \vec{b}$ orthogonal to $\vec{a}$ \begin{align}\vec{a} \cdot \vec{... perp \vec{a}$. For $\vec{a} \times \vec{b}$ orthogonal to $\vec{b}$ \begin{align}\vec{b} \cdot \vec{
- Question 4 and 5 Exercise 3.3
- t{i}+\hat{j}-\hat{k}$. Find a vector that is orthogonal to both $\vec{a}$ and $\vec{b}$. ====Solution=... =\vec{a} \times \vec{b}$ is a vector that is orthogonal to both $\vec{a}$ and $\vec{b}$. Therefore, \b... endicular to both $\vec{a}$ and $\vec{b}$. ====Go To==== <text align="left"><btn type="primary">[[m
- Question 2 and 3 Exercise 3.3
- +2=0\end{align} $ \vec{a}$ and $\vec{b}$ are orthogonal. \\ $$\Rightarrow \theta=90^{\prime \prime}$$... 99^{\circ}\text{(approximately)}\end{align} ====Go To==== <text align="left"><btn type="primary">[[m
- Question 11, Exercise 3.3
- b}|^2\\ 14+21&=35\\ 35&=35\end{align} Thus by Pytagorous theorem, the vectors $\vec{a}, \vec{b}$ and $... ight angle triangle is also isosceles. ====Go To==== <text align="left"><btn type="primary">[[m
- Question 1, Exercise 3.2
- ec{b}|}$. $ ====Solution==== Solve yourself. ====Go to ==== <text align="left"><btn type="success">[[
- Question 2, Exercise 3.2
- }{2}\hat{j}$$ \\ Which is the unit vector. ====Go To==== <text align="left"><btn type="primary">[[m
- Question 3 & 4, Exercise 3.2
- t{21}\end{align} Thus $$x=-2\pm\sqrt{21}.$$ ====Go To==== <text align="left"><btn type="primary">[[m
- Question 5 & 6, Exercise 3.2
- $ Hence coordinates of $D$ are $(-3,-2)$. ====Go To==== <text align="left"><btn type="primary">[[m
- Question 7, Exercise 3.2
- (1,-2,3)$. ====Solution==== Do yourself. ====Go To==== <text align="left"><btn type="primary">[[f
- Question 7, Exercise 3.2
- (1,-2,3)$. ====Solution==== Do yourself. ====Go To==== <text align="left"><btn type="primary">[[m
- Question 9 & 10, Exercise 3.2
- ghtarrow{OR}&=-3\hat{i}+3\hat{k}\end{align} ====Go To==== <text align="left"><btn type="primary">[[m
- Question 11, Exercise 3.2
- ghtarrow{OK}&=6\hat{i}+17\hat{j}\end{align} ====Go To==== <text align="left"><btn type="primary">[[m