If the vectors c, a=x i+y j+z k and b= j are such that a, c, b form a right handed system,…

Question

If the vectors $\vec c$, $\vec a=x\hat i+y\hat j+z\hat k$ and $\vec b=\hat j$ are such that $\vec a,\vec c,\vec b$ form a right handed system, then $\vec c$ is:

Accepted Answer

For a right-handed system $(\vec a,\vec c,\vec b)$, $\vec c=\vec b\times\vec a$:

$$\vec c = \begin{vmatrix}\hat i&\hat j&\hat k\0&1&0\x&y&z\end{vmatrix} = z\hat i-x\hat k$$

Solutions · 1