Question

28. A and B are two vectors given by A = 2i -j and B-i-j. Find the magnitude of the component
of A along B and B along A.
int​

Answer 1

Answer:

1/$\sqrt{2$

Explanation:

The angle between given two vectors is,

Cosθ= (vectorA·vectorB) / ( |vectorA|·|vectorB| ) = (2×-1)+(-1×-1) / ($\sqrt{4+1}$)($\sqrt{1+1}$)

Cosθ= -1/$\sqrt{10}$

Componenet of vectA along vectB = vectorA Cosθ

=(-1/$\sqrt{10}$) (2i -j)

= -2/$\sqrt{10}$ i + 1/$\sqrt{10}$ j

∴It's magnitude = $\sqrt{(4/10)+(1/10)$

                          =1/$\sqrt{2}$

Thank you!