Let \vec{a}= \hat{i}+2\hat{j}-3\hat{k} and \vec{b}= 3\hat{i}-\hat{j}+2\hat{k}  be two vectors. Show that the vectors \left ( \vec{a}+\vec{b} \right ) and \left ( \vec{a}-\vec{b} \right ) are perpendicular to each other.

 

 

 

 
 
 
 
 

Answers (1)

Now \left ( \vec{a}+\vec{b} \right )\cdot \left ( \vec{a}-\vec{b} \right )= \vec{a}\cdot \vec{a}-\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{a}-\vec{b}\cdot \vec{b}
                                             = \left | a \right |^{2}-\left | \vec{b} \right |^{2}={\left | \hat{i}+2\hat{j}-3\hat{k} \right |}^2-{\left | 3\hat{i}-\hat{j}+2\hat{k} \right |}^2
                                             = \left ( 1+4+9 \right )-\left ( 9+1+4 \right )= 0
Hence, \vec{a}+\vec{b}  & \vec{a}-\vec{b}  are perpendicular to each other. 

Most Viewed Questions

Related Chapters

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Expert Mentorship, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions