A unit vector in xy plane that makes an angle 45 degree with the vector i+j and an angle 60 degree with the vector 3i-4j is

Answers (1)

Solution:    

                    vecp=ahati+b hatjRightarrow left | vecp 
ight |=1Rightarrow a^2+b^2=1.

            Rightarrow      (ahati+bhatj)(hati+hatj)=left | ahati+bhatj 
ight |left | hati+hatj 
ight |cos 45^circ

                        a+b=sqrta^2+b^2	imes sqrt2	imes frac1sqrt2

                        a+b=1               ..........(1)

             Rightarrow        (ahati+bhatj)(3hati-4hatj)=left | ahati+bhatj 
ight |left | 3hati-4hatj 
ight |cos 60^circ

                          3a-4b=5	imes frac12            .......(2)

               Sloving   (1)    and   (2)  We get 

              Hence ,       a=frac1314, b=frac114

Most Viewed Questions

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