# Math Help - component of one vector in the direction of another

1. ## component of one vector in the direction of another

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

2. Originally Posted by hmmmm
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 $\vec w = (w_1, w_2)$:

$(2,1) \cdot \vec w = 0~\implies~ \vec w = (w_1,-4w_1)$

2. Now use the given equation:

$\lambda \cdot (4,1) + (w_1, -4w_1)=(2,1)$

Solve for $\lambda$ and $w_1$

3. Make a sketch to control your calculations.