Find the component of c = <2, 1> in the direction v = <4, 1>. Hence
write c in the form c = λv + w, where v · w = 0.
Check also that w itself is the component of c in the direction w.
thanks for any help
Find the component of c = <2, 1> in the direction v = <4, 1>. Hence
write c in the form c = λv + w, where v · w = 0.
Check also that w itself is the component of c in the direction w.
thanks for any help
1. Calculate the direction of $\displaystyle \vec w = (w_1, w_2)$:
$\displaystyle (2,1) \cdot \vec w = 0~\implies~ \vec w = (w_1,-4w_1)$
2. Now use the given equation:
$\displaystyle \lambda \cdot (4,1) + (w_1, -4w_1)=(2,1)$
Solve for $\displaystyle \lambda$ and $\displaystyle w_1$
3. Make a sketch to control your calculations.