- #1
Hijaz Aslam
- 66
- 1
Homework Statement
Given ##\vec{A}=2\hat{i}+3\hat{j}## and ##\vec{B}=\hat{i}+\hat{j}##.Find the component of ##\vec{A}## along ##\vec{B}##.
Homework Equations
##\vec{A}.\vec{B}=ABcosθ## where θ is the angle between both the vectors.
The Attempt at a Solution
I attempted the question as follows:
Let the angle between ##\vec{A}## and ##\vec{B}## be 'θ'. So the component of ##\vec{A}## along ##\vec{B}## is given by ##Acosθ\hat{B}## => ##Acosθ(\frac{\vec{B}}{B})##
As ##\vec{A}.\vec{B}=ABcosθ## => ##[( 2\hat{i}+3\hat{j})(\hat{i}+\hat{j})]/B=Acosθ## => ##\frac{5}{\sqrt{2}}=Acosθ##
Therefore the component is : ##\frac{5}{\sqrt{2}}(\frac{\hat{i}+\hat{j}}{\sqrt{2}})## => ##\frac{5}{2}({\hat{i}+\hat{j}})##
But my text produces the solution as follows:
##A_B=(\vec{A}.\vec{B})\hat{B}=\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})##.