Vector properties with multiplication

Question

Let $a,b,c \in \Bbb R^3$ such that $a \cdot c = 1$ and $a \cdot b = −1$. Show that $a \times ( b \times c) = b + c$.

I tried to substitute in $a = (1,0,0)$, $b = (1,0,0)$, $c = (-1,0,0)$ but it didn't work. What am I doing wrong?

Answer 1

Hint: use the vector triple product formula $a \times (b \times c) = b (a \cdot c) - c (a \cdot b)$.

Answer 2

Let $a,b,c \in \Bbb R^3$ such that $a \cdot c = 1$ and $a \cdot b = −1$. Show that $a \times ( b \times c) = b + c$.

I tried to substitute in $a = (1,0,0)$, $b = (1,0,0)$, $c = (-1,0,0)$ but it didn't work. What am I doing wrong?

You have $a\cdot c= -1$ and $a\cdot b=1$