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

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- Apr 21st 2010, 03:22 PMhmmmmcomponent 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 - Apr 21st 2010, 11:28 PMearboth
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.