SATHEE: Kinematics Question 115

Kinematics Question 115

Question: The vectors from origin to the points A and B are $\vec{A} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ and $\vec{B} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ respectively. The area of the triangle OAB be

Options:

A) $\frac{5}{2} \sqrt{17}$ sq.unit

B) $\frac{2}{5} \sqrt{17}$ sq.unit

C) $\frac{3}{5} \sqrt{17}$ sq.unit

D) $\frac{5}{3} \sqrt{17}$ sq.unit

Show Answer

Answer:

Correct Answer: A

Solution:

Given $\vec{O A} = \vec{a} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ and $\vec{O B} = \vec{b} = 2 \hat{i} + \hat{j} - 2 \hat{k}$
$∴ (\vec{a} \times \vec{b}) = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & - 6 & 2 \\ 2 & 1 & - 2 \end{matrix} |$

$= (12 - 2) \hat{i} + (4 + 6) \hat{j} + (3 + 12) \hat{k}$

$= 10 \hat{i} + 10 \hat{j} + 15 \hat{k}$
$\Rightarrow | \vec{a} \times \vec{b} | = \sqrt{10^{2} + 10^{2} + 15^{2}}$

$= \sqrt{425}$

$= 5 \sqrt{17}$ Area of $Δ O A B = \frac{1}{2} | \vec{a} \times \vec{b} | = \frac{5 \sqrt{17}}{2}$ sq.unit.

Play Store

App Store

Ask SATHEE

Welcome to SATHEE !
Select from 'Menu' to explore our services, or ask SATHEE to get started. Let's embark on this journey of growth together! 🌐📚🚀🎓

I'm relatively new and can sometimes make mistakes.
If you notice any error, such as an incorrect solution, please use the thumbs down icon to aid my learning.
To begin your journey now, click on "I understand".

Kinematics Question 115

Question: The vectors from origin to the points A and B are A→=3i^−6j^+2k^ and B→=2i^+j^−2k^ respectively. The area of the triangle OAB be

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

Question: The vectors from origin to the points A and B are $\vec{A} = 3 \hat{i} - 6 \hat{j} + 2 \hat{k}$ and $\vec{B} = 2 \hat{i} + \hat{j} - 2 \hat{k}$ respectively. The area of the triangle OAB be