Question

Let
$\vec{a}=\hat{i} - 2\hat{j} + 3\hat{k}, \vec{b}=\hat{i} - \hat{j} + \hat{k}$ and $\vec{c}$
be a vector such that
$\vec{a} + (\vec{b}×\vec{c}) = \vec{0}$ and $\vec{b}.\vec{c} = 5.$
Then the value of 3($\vec{c}.\vec{a}$) is equal to

Answer 1

The correct answer is 0
Data contradicts
$∵ \vec{a}.\vec{b} = 1 - 2 + 3 = 2$ [ According to $\vec{a}$ and $\vec{b}$ ]
But it is given that
$\vec{a} + (\vec{b}×\vec{c}) = 0$
$\vec{a} = - (\vec{b} × \vec{c})$
$⇒ \vec{a} ⊥ \vec{b}$ $and$ $\vec{a} ⊥ \vec{c}-$
$∴ \vec{a}.\vec{b} = 0$