If and are the position vectors of the vertices of a triangle , then the area of the triangle is:

Explanation: Correct Option: (a)

How do I solve NIMCET 2015 Mathematics questions?

Practice NIMCET 2015 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

What is the difficulty level of NIMCET Mathematics questions?

NIMCET Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Are NIMCET previous year papers available for free?

Yes. Mathem Solvex provides free access to NIMCET previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

+91 99359 65550 contact@maarula.in

Mathem SolvexGet the solution of every question

Home

Previous Year Questions

NIMCET CUET PG JAMIA MAH-CET AMU VITMEE

PYQ Paper Downloads Practice Paper

Latest Update

Resources

PYQ PDF Downloads Our Courses Test Series About Us

Home

Question Archive

Explore All PYQs NIMCET CUET PG JAMIA MAH-CET AMU VITMEE

Downloads & Practice

PDF Material Downloads Solve Practice Paper

Quick Links

Latest Updates About Us Our Premium Courses Contact Support

Preparing for Excellence...

MAARULA CLASSES

MCA Entrance Coaching

Quick Links

Home
Blog
About
Contact Us
Faculty

Exams

NIMCET
CUET PG
VITMEE
JAMIA
MAH-CET

Free Resources

Previous Year Papers
Free Mock Tests
Strategy Videos
Syllabus

Our Courses

Live Classes
Test Series
Comprehensive Notes

Download Maarula Mathem App

For Seamless learning experience

Google Play

Designed & Developed with ❤️ by Vivek Kumar | LinkedIn

Home PYQs

Updates Resources About

NIMCET 2015 Mathematics PYQ — If and are the position vectors of the vertices of a triangle , t… | Mathem Solvex | Mathem Solvex

Home
Questions
NIMCET
Mathematics
Q. 4147

Tip:A–D to answerE for explanationV for videoS to reveal answer

NIMCET 2015 — Mathematics PYQ

NIMCET | Mathematics | 2015

If $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of the vertices $A, B, C$ of a triangle $ABC$ , then the area of the triangle $ABC$ is:

Choose the correct answer:

A.
$\frac{1}{2} |\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}|$

Correct Answer:

$\frac{1}{2} |\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}|$

Explanation

\text{Area of } \triangle ABC = \frac{1}{2} |\vec{AB} \times \vec{AC}|

\vec{AB} = \vec{b} - \vec{a}

\vec{AC} = \vec{c} - \vec{a}

\text{Area} = \frac{1}{2} |(\vec{b} - \vec{a}) \times (\vec{c} - \vec{a})|

\text{Area} = \frac{1}{2} |\vec{b} \times \vec{c} - \vec{b} \times \vec{a} - \vec{a} \times \vec{c} + \vec{a} \times \vec{a}|

\vec{a} \times \vec{a} = 0

- \vec{b} \times \vec{a} = \vec{a} \times \vec{b}

- \vec{a} \times \vec{c} = \vec{c} \times \vec{a}

\text{Area} = \frac{1}{2} |\vec{b} \times \vec{c} + \vec{a} \times \vec{b} + \vec{c} \times \vec{a}|

\text{Area} = \frac{1}{2} |\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}|

Correct Option: (a)

Explanation

\text{Area of } \triangle ABC = \frac{1}{2} |\vec{AB} \times \vec{AC}|

\vec{AB} = \vec{b} - \vec{a}

\vec{AC} = \vec{c} - \vec{a}

\text{Area} = \frac{1}{2} |(\vec{b} - \vec{a}) \times (\vec{c} - \vec{a})|

\text{Area} = \frac{1}{2} |\vec{b} \times \vec{c} - \vec{b} \times \vec{a} - \vec{a} \times \vec{c} + \vec{a} \times \vec{a}|

\vec{a} \times \vec{a} = 0

- \vec{b} \times \vec{a} = \vec{a} \times \vec{b}

- \vec{a} \times \vec{c} = \vec{c} \times \vec{a}

\text{Area} = \frac{1}{2} |\vec{b} \times \vec{c} + \vec{a} \times \vec{b} + \vec{c} \times \vec{a}|

\text{Area} = \frac{1}{2} |\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}|

Correct Option: (a)

Same Topic Questions

NIMCET

The vector $A = (2 x + 1) \hat{i} + (x^{2} - 6 y) \hat{j} + (x y^{2} + 3 z) \hat{k}$ is …

(Correct Answer)

B.
$|\vec{a} \times \vec{b}|$

C.
$\frac{1}{2} |\vec{a} \times \vec{b} - \vec{b} \times \vec{c} - \vec{c} \times \vec{a}|$

D.
$|\vec{a} \times (\vec{b} \times \vec{c})|$

NIMCET
A man starts at the origin $O$ and walks a distance of $3$ units in the north-east direct…

NIMCET
The value of $m$ for which volume of the parallelopiped is 4 cubic units whose three edge…

NIMCET
The number of distinct real values of $λ^{2} \hat{i} + \hat{j} + \hat{k}$ , $\hat{i} +…

NIMCET
If $\vec{a}, \vec{b}$

Explore More

TopicAll "Vector" PYQs →SubjectMore Mathematics Questions →YearNIMCET 2015 Paper →All NIMCET Questions →📄 Download NIMCET PYQ Papers →📝 Preparation Tips & Articles →