Question

Find the components of a vector A = 2hati + 3hatj along the directions of hati + hatj and hati - hatj.

Answer 1

The component of vector A along vector B and C is:

• Given, A = (2 i + 3 j) ,  B = (i + j) and C = (i - j)

• Component of A along B = $\frac{A.B}{|B|}$ =$\frac{(2 i + 3 j).(i + j)}{\sqrt{2}} = \frac{2+3}{\sqrt{2}} = \frac{5}{\sqrt{2} }$

• Component of A along C = $\frac{A.C}{|C|}$ =$\frac{(2 i + 3 j).(i - j)}{\sqrt{2}} = \frac{2-3}{\sqrt{2}} = \frac{-1}{\sqrt{2} }$