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$\therefore$ The girl’s displacement from her initial point of departure is $=\frac{-5}{3}\hat{i}+\frac{\mathrm{3\surd 3}}{2}\hat{j}$

Hi, listed below are the top M.Tech Robotics Engineering colleges in India according to NIRF ranking for the year 2024:

Hope this helps!

Given,

Point $P(x_1,y_1,z_1)\&Q(x_2,y_2,z_2)$

$\overrightarrow{PQ}$ = Position vector of Q.- Position vector of P

$=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}+(z_2-z_1)\hat{k}$

IIT Madras offers various BTech and BTech Integrated courses via JEE Advanced exam scores. Candidates belonging to SC and ST categories acquiring a rank of 850 can get admission to various BTech courses under SC and ST AI quota. Candidates can find those courses separately for ST and SC quota both from the table below:

Courses offered under 850 rank for SC AI category candidates:

Courses offered under 850 rank for ST AI category candidates:

Hi, listed below are the eligibility criteria for admission to the best colleges for M.Tech in Robotics Engineering in India:

• Students who have a BTech degree in Mechanical Engineering, Robotics Engineering,  Electrical Engineering, CSE, or a related field with at least 55 percent marks.

Disclaimer: This information is sourced from official website and may vary.

Let $\overrightarrow{r}$ be unit vector in the XY-plane then,  $\overrightarrow{r}=cos\theta \hat{i}+sin\theta \hat{j}$

$\theta$ is the angle made by the unit vector with the positive direction of the X-axis.

Then,  $\theta =30^0$

$\therefore$ ReQ.uired unit vector $=\frac{}{2}\hat{i}+\frac{1}{2}\hat{j}$

To get into Saveetha College of Architecture and Design for BArch course, candidates must meet the eligibility criteria set by the institute. Students must pass Class 12 with Physics, Maths and Chemistry. Saveetha College of Architecture and Design offers full-time BArch courses of five years' duration. Students can get into this course based on entrance-exam. 

(c) Given,

$\begin{array}{l}A=-\widehat{i}+\frac{1}{2}\widehat{j}+4\widehat{k}\\ B=\widehat{i}+\frac{1}{2}\widehat{j}+4\widehat{k}\\ C=\widehat{i}-\frac{1}{2}\widehat{j}+4\widehat{k}\\ D=-\widehat{i}-\frac{1}{2}\widehat{j}+4\widehat{k}\\ A\overrightarrow{B}=\left(1+1\right)\widehat{i}+\left(\frac{1}{2}-\frac{1}{2}\right)\widehat{j}+\left(4-4\right)\widehat{k}\\ =2\widehat{i}\\ B\overrightarrow{C}=\left(1-1\right)\widehat{i}+\left(-\frac{1}{2}-\frac{1}{2}\right)\widehat{j}+\left(4-4\right)\widehat{k}\\ =-\widehat{j}\end{array}$

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• Class 10 and 12 marksheets
• A bachelor's degree (if applicable)
• A valid ID proof (Adhaar, PAN Card, Passport, etc.)
• 2 Passport-sized photographs
• Migration certificate
• Caste Certificate (if any).

(B) Given,

$\therefore$ Hence,  $\overrightarrow{a}\times \overrightarrow{b}$ is a unit vector if angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{4}$

Given,

$\begin{array}{l}\overrightarrow{a}=\widehat{i}-\widehat{j}+3\widehat{k}\\ \overrightarrow{b}=2\widehat{i}-7\widehat{j}+\widehat{k}\end{array}$

The area of a parallelogram with $\overrightarrow{a}$ and $\overrightarrow{b}$ as its adjacent sides is given by $\left|\overrightarrow{a}\times \overrightarrow{b}\right|$

Hi, you can surely go for M.Tech in Robotics Engineering in India as there are 90+ best M.Tech in Robotics Engineering colleges in India,  out of which 60+ colleges are owned privately and 20+ colleges are owned by the government. GATE, CUET PG, Karnataka PGCET, TS PGECET, Andhra Pradesh PGECET, etc. are the top M.Tech in Robotics Engineering colleges in India. IIT Delhi, SRMIST Kattankulathur, Chandigarh University, Jadavpur University, IIT Roorkee, IIT Guwahati and IIT Mandi are the top colleges for M.Tech in Robotics Engineering in India.

George Mason Univeristy is a public university that operates with the aim of making quality education accessible to all members of the student community. Its acceptance rate of 90% is in-line with that goal.

However, admission at the institute should not be taken for granted & prospective students must still satisfy its GPA requirement or equivalent that stands at 3.0 on a 4.0 scale while also securing acceptable scores in their language test scores to have a good chance of admisssions to GMU.

Given,

$A\left(1,1,2\right),B\left(2,3,5\right)C\left(1,5,5\right)$

We have,

$\begin{array}{l}A\overrightarrow{B}=\widehat{i}+2\widehat{j}+3\widehat{k}\\ A\overrightarrow{C}=4\widehat{j}+3\widehat{k}\end{array}$

The area of given triangle is $\frac{1}{2}\left|A\overrightarrow{B}\times A\overrightarrow{C}\right|$

4. Given, f (x) = x n > n = positive.

At x = 2,

(x) = n.

$\underset{x\to n}{lim}$ f (x) = $\underset{x\to n}{lim}$ x n = n

∴ $\underset{x\to n}{lim}$ f (x) = f (x)

So f is continuous at x = n.

We take any parallel non- zero vectors so that $\overrightarrow{a}\times \overrightarrow{b}=0$ .

Given,

$\begin{array}{l}\overrightarrow{a}=a_1\widehat{i}+a_2\widehat{j}+a_3\widehat{k}\\ \overrightarrow{b}=b_1\widehat{i}+b_2\widehat{j}+b_3\widehat{k}\\ \overrightarrow{c}=c_1\widehat{i}+c_2\widehat{j}+c_3\widehat{k}\\ \therefore \left(\overrightarrow{b}+\overrightarrow{c}\right)=\left(b_1+c_1\right)\widehat{i}+\left(b_2+c_2\right)\widehat{j}+\left(b_3+c_3\right)\widehat{k}\\ Now,\end{array}$

$\begin{array}{l}=\widehat{i}\left\{a_2\left(b_2+c_3\right)-a_3\left(b_2+c_2\right)\right\}-\widehat{j}\left\{a_1\left(b_3+c_3\right)-a_3\left(b_1+c_1\right)\right\}\\ +\widehat{k}\left\{a_1\left(b_2+c_2\right)-a_2\left(b_1+c_1\right)\right\}\\ =\widehat{i}\left\{a_2{b}_2+a_2{c}_3-a_3{b}_2-a_3{c}_2\right\}-\widehat{j}\left\{a_1{b}_3+a_1{c}_3-a_3{b}_1-a_3{c}_1\right\}\\ +\widehat{k}\left\{a_1{b}_2+a_1{c}_2-a_2{b}_1-a_2{c}_2\right\}----(1)\end{array}$

$\begin{array}{l}=\widehat{i}\left(a_2{b}_3-a_3{b}_2\right)-\widehat{j}\left(a_1{b}_3-a_3{b}_1\right)+\widehat{k}\left(a_1{b}_2-a_2{b}_1\right)----(2)\\ And,\end{array}$

=

$\widehat{i}\left(a_2{c}_3-a_3{c}_2\right)-\widehat{j}\left(a_1{c}_3-a_3{c}_1\right)+\widehat{k}\left(a_1{c}_2-a_2{c}_1\right)----(3)$

Adding (2) and (3), we get

$\begin{array}{l}\left(\overrightarrow{a}\times \overrightarrow{b}\right)+\left(\overrightarrow{a}\times \overrightarrow{c}\right)=\widehat{i}\left(a_2{b}_3-a_3{b}_2\right)-\widehat{j}\left(a_1{b}_3-a_3{b}_1\right)+\widehat{k}\left(a_1{b}_2-a_2{b}_1\right)\\ +\widehat{i}\left(a_2{c}_3-a_3{c}_2\right)-\widehat{j}\left(a_1{c}_3-a_3{c}_1\right)+\widehat{k}\left(a_1{c}_2-a_2{c}_1\right)\\ \left(\overrightarrow{a}\times \overrightarrow{b}\right)+\left(\overrightarrow{a}\times \overrightarrow{c}\right)=\widehat{i}\left(a_2{b}_3-a_3{b}_2+a_2{c}_3-a_3{c}_2\right)+\widehat{j}\left(-a_1{b}_3+a_3{b}_1-a_1{c}_3+a_3{c}_1\right)\\ +\widehat{k}\left(a_1{b}_2-a_2{b}_1+a_1{c}_2-a_2{c}_1\right)\\ =\widehat{i}\left(a_2{b}_3+a_2{c}_3-a_3{c}_2-a_3{b}_2\right)-\widehat{j}\left(a_1{b}_3+a_1{c}_3-a_3{b}_1-a_3{c}_1\right)\\ +\widehat{k}\left(a_1{b}_2+a_1{c}_2-a_2{b}_1-a_2{c}_1\right)-----(4)\end{array}$

From (1) and (4), we have

$\overrightarrow{a}\left(\overrightarrow{b}+\overrightarrow{c}\right)=\overrightarrow{a}\times \overrightarrow{b}+\overrightarrow{a}\times \overrightarrow{c}$

Hence, proved.

IIT Madras accepts JEE Advanced scores. If we talk about the IIT Madras 2023 cutoff, candidates had witnessed lenient cutoffs as compared to IIT Madras JEE Advanced cutoff 2024. Further, it is possible to get into IIT Madras at a 7000 rank in JEE Advanced but at this rank, candidates won't be able to opt for top specialisations such as ECE, Civil, Mechanical etc. Check out the table below for specialisations available at IIT Madras under this rank.