Question

The uknown vector \(v\) satisfyes \(b\cdot v=\lambda\) and \(b \times v =c\) . Express v in terms of \(\lambda\), b and c

Answer 1

The uknown vector \(v\) satisfyes \(b\cdot v=\lambda\) and \(b \times v =c\) . Express v in terms of \(\lambda\), b and c

Answer 2

I tryed using \((\vec{b} \times \vec{v})^2=b^2v^2-(\vec{b} \cdot \vec{v})^2\),
but no success

Answer 3

I have a class to get to in a few minutes, but I've tried assuming the vectors belong to \(\mathbb{R}^3\) and trying to generalize from there... If I have a moment later, I'll get back to it.

By the way, are you having problem seeing the TeX?

Answer 4

No . It is fine now. I see it correctly

Answer 5

@ganeshie8 , @campbell_st any ideas?

Answer 6

Projection of \(\large v\) along \(\large b\) : \[\large \dfrac{b^Tv}{b^Tb} b = \dfrac{\lambda }{b^Tb} b\]

Answer 7

The perpendicular vector \(e\) can be given by : \[\large e = v- \dfrac{\lambda }{b^Tb} b \]