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Vector Question

Hello,
I'm currently stuck with this vector question .... :s-smilie:

I just cant see how to find λ \lambda in terms of pp and cc

Here is the question:

Find s in terms of p and c for:

∣s⃗−c⃗∣=1 |\vec{s} - \vec{c}| = 1
s⃗=λp⃗ \vec{s} = \lambda \vec{p}

You may find it useful to use the constant: α=(p⃗⋅c⃗)2−p⃗2(c⃗2−1) \alpha = (\vec{p} \cdot \vec{c})^2 - \vec{p}^2 (\vec{c}^2 - 1)

It would be great if someone could help me :smile:
Reply 1
Avatar for vvidetta
vvidetta
|s-c|^2=1
but |s-c|^2=(s-c).(s-c)
=s.s-2s.c+c.c
=(lp).(lp)-2(lp).c+c.c (since s=lp)
=l^2(p.p)-2l(p.c)+c.c=1

where I'm using l for lambda. Solve the above equation for lambda and substitute into s. Hope that helps :smile:
Reply 2
Avatar for darkness9999
darkness9999
OP
9
vvidetta
|s-c|^2=1
but |s-c|^2=(s-c).(s-c)
=s.s-2s.c+c.c
=(lp).(lp)-2(lp).c+c.c (since s=lp)
=l^2(p.p)-2l(p.c)+c.c=1

where I'm using l for lambda. Solve the above equation for lambda and substitute into s. Hope that helps :smile:


thank you !! +REP !

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