Please solve RD Sharma class 12 chapter Vector or Cross Product exercise 24.1 question 37 maths textbook solution

Answers (1)

Answer:

 4

Hint: To solve this we use |\vec{a} \times \vec{b}|,|\vec{a} \cdot \vec{b}| formula

Given: |\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=400

Solution:

\begin{aligned} &|\vec{a} \times \vec{b}|=|\vec{a}| \times|\vec{b}| \sin \theta \\\\ &|\vec{a} \cdot \vec{b}|=|\vec{a}| \times|\vec{b}| \cos \theta \\\\ &|\vec{a}|^{2}|\vec{b}|^{2} \sin ^{2} \theta+|\vec{a}|^{2}|\vec{b}|^{2} \cos ^{2} \theta=400 \end{aligned}

\begin{aligned} &|\vec{a}|^{2}|\vec{b}|^{2}\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=400 \\\\ &|\vec{a}|^{2}|\vec{b}|^{2}=400 \\\\ &|\vec{b}|^{2}=\frac{400}{|\vec{a}|^{2}}=\frac{400}{5^{2}}=\frac{400}{25} \end{aligned}

\begin{aligned} &|\vec{b}|^{2}=16 \\\\ &|\vec{b}|=4 \end{aligned}

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions